WEBVTT

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Oh, okay, good afternoon class. So this is engineering probability class 2008 and.

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My usual question is, can you hear me.

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Because again, beautiful Thank you. And again, if anything happens, if I suddenly cut out, please tell me I have.

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Open so so.

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What are we going on today? We're talking about 12 some examples and continuing on chapter 1 chapter 2 and also following along.

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I'll write some stuff on the on the pad and upload it.

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And maybe get some real world stuff.

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So 1st, if anyone's been following the news lately, it's been.

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A stock market fun, you know, it's a game stop company.

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And so, if you're trying to use probability to say, make money in the stock market, you might want to see, could it explain what's happening with game if you don't know what's happening here?

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You may 500 bucks. Cool. Congratulations, Andrew.

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If we, if we were over 21 and could meet in person, I'd say a bias to drink, but.

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We'll just stop. Congratulations.

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Hey, okay that was not alcoholic by the way.

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So 1st file stuff you may notice at the top here. I added a button and this.

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Shows you things like it's my attempt to do is chat and.

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Transcripts and so on and media site has the.

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Oh, okay. That's number 1 number 2.

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Probability in the real world people like to try to use powerful mathematics to.

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To predict say the stock market,

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and Paul Krugman got a Nobel memorial prize and economic science some years ago and he was in the press a lot of comments on politics and article column in the New York Times,

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and so on and it makes a valid point.

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Here is that they do this beautiful, sophisticated mathematics equations with lots of variables, Greek letters and them and so on nicely typeset.

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The vital trivial little detail is it may not match reality.

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And if that's important to you, then.

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You know, keep that in mind that just because an equation is too complicated for you to understand. It doesn't always mean that is right.

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And relevance thing, this has also been observed by some people.

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Jamie diamond who's head of 1 of the largest banks in the world has made comments observed that.

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The stock market moves has larger variations and the math would predict.

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So, and another thing is that people assume that things like the stock market that there's some mean, and that things will converge towards the mean and the long term that may not be true for things like the stock market. So.

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Mathematically is that statistics? Like the variants may actually not be computable.

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Um, they're into girls that diverged. Okay.

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But for things we're going to cover in this course they do converge to.

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A, they converge to some mean if you toss a fair coin, then it.

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It converges it convert just to, um, to 50, 50. now.

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Um, for example.

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I mean, if I have a coin, something like.

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Whereas here, you know, I could be tossing in actual coin.

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And so on, but that takes a long time. So Here's an app that does it.

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And with this app, I've done.

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I could say we'll make it a fair coin.

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Avatar set, and maybe 10 times and.

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And this happened to come up heads. Exactly. 5 entails exactly 5. um.

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Try a 2nd time, 7 and 3 a 3rd time.

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4 and 6, Emmy, 10 coins. 1010 times.

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And you say it's from each each time, I talked to coin 10 times and repeated this 10 times, the number of heads range from 2 to 7 out of 10.

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I repeated it 100 times.

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Number of heads and, you know.

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Generally, 4 to 6 or 7 is the broad thing that's for 10 toss. Now if I do 100 tosses, it's going to be convert. It's going to be a lot tighter. You see here.

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You know, there's a serious number of from 3 to 7 heads. Maybe now cost 100 times. It's more clustered from.

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44 to 6 state, it's a lot closer. Say, 4.

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40% to 60%. If I toss the coin a 1000 times.

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It's more like from 48 to 52% if I tossed the coin 10000 times.

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It's more from 49% to 51%.

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So, the larger the experiment is the more tightly clustered as a percentage.

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Are the number of heads? This is a lot of large numbers so an example might be if you look at all the molecules of air in my room here, quite a few of them as a few moles of them. Who knows? There might be kind of the 24th, 10 of the 21st molecules of air.

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Perhaps, if each molecule independently decided, is it going to be left, or right half of the room, the probability that they're all going to be the left half the room's going to be really small.

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So, okay, so we got that thing there. Um.

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I want to draw on some other probability things talking about just an application of probability and channels and unreliable channels. I'm going to do this, like, slightly different numbers to help you understand it.

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Here and.

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Si.

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I can get in touch bigger for you.

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Not really.

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It has just.

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My Web cam out just crashed on me.

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Can get rather annoyed at software.

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Hardware and what manifest restart the web cam app.

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Silence.

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Okay.

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Well, maybe I won't.

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Was working a minute or 2 a little reluctant to play with the webx.

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I say.

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Silence.

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My laptop, I'm on a 2nd laptop.

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Silence.

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Silence.

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Okay.

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Let's see if this works.

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Silence.

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Silence.

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Silence.

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Silence.

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Silence.

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Silence.

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Silence.

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Good.

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Silence.

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Okay.

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Silence.

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Crazy thing is a laptop, which is locked up and then something weird happen is a new laptop. The laptop Ahmad now is like a 6 year old laptop. Okay.

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So, we.

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To motivate probability and do some simple.

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Some simple calculations.

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You're using a continually example of transmission over an unreliable channel.

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And this is a theme that we will have throughout the whole semester actually, because we can do math on it.

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I mentioned, we'll probably look at later in the course is trying to get assigned probabilities to what the transmitted was.

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Given that you received a certain bet. Now, here, I'm not going to be completely so complicated take an easier version of that.

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We want to transmit a bit it's going to be 0T or a 1 pair and.

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99.9% of the time it arrives correctly and 1% of the time it arrives wrong.

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And here, I'm making things simpler. I'm assuming it's symmetric that zeros and ones have the same probability of going bad in the real world. That might not be true.

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And you might arrive more correctly that i1 goes in the real world. Some weird things happen.

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Okay, so I'm going to use a really simple transmission method here.

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And just going to transmit every bit 3 times.

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And then the receiver will vote best 2 out of 3.

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And so if you receive receive 0, 0 0.

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Well, guess it wasn't cereal it was transmitted if the receiver gets 0 0T and a run 0T was transmitted, because it saw 2 zeros and a run.

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However, if the receiver receives, is there a rod 1 we'll assume that a 1 was transmitted.

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Now, so what I'm trying to do is.

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See, how reliable this channel is now.

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The 1st, the raw channel had another point 1% of the time. So what I'm doing now is I'm saying, maybe I've got lots of bandwidth and used in the channel and we'll just send it 3 times. No, no sophisticated error correcting cards.

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No, read Solomon codes and stuff like that.

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Really simple, but the question is, how much more reliable is this method a chance to.

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Do some simple numbers well, and used the credibility of an error at some point 1% at the time.

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Now, so each bit arrives correctly 99.9% of the time. So, 3 beds will all arrive correctly with that number. Cute the 1st, that arrives correctly. 2nd bit. And the 3rd that.

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And here I'm bringing in some simple probability that if I have some independent events that don't affect each other, then the probability of the combo them as the product of the probabilities starts getting into that.

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And.

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Some of the videos I'm pointing you to watch, so.

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It's intuitively correct that if.

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These things to be 2 events, some of the 1st bit arriving correct? And the 2nd debt arriving correct? The 2 events if they don't affect each other and.

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You can start asking now, could they be correlated perhaps of some common.

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Carbon, I don't know a sharp bites into the submarine cable or something and.

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Something weird like that. Then sharks have been known to do that by the way they dragged up a submarine, but some years ago, they had it broken off to embed it in it.

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Okay, getting beyond this course a little while it was the next level of detail.

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Is that the cable had repeated and savvy.

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20 miles or something that were powered by a D. C voltage with the DC voltage that was sent through the cable and that, of course induced every kinetic field around the cable that attracted the shark. Okay. Getting back to here.

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So, 3 bets will all arrive correctly and I completed it there.

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So you don't have to worry about that. It's point 9, 9, which is 9, 9, 7 and so, 3 bits are arriving correctly less likely than 1 bed arrive incorrectly. It's supposed to arrive correct? And also the 2nd, but, and also the 3rd.

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Well, what about the chance that of the 3 transmitted? Bits? 1 of them was bad and 2 of them were good.

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There's 3 ways that could happen the 1st bit might be bad and the 2nd and 3rd beds. Good.

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The 1st trip might be good. The 2nd bit bad. The 3rd could.

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The 1st, 2 bits might be good in the bad, bad.

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And the probability of their being exactly 1 error is the number have there it's front of or.

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2 9, 9, 4% so the pedagogy of good. Good bad is probably 99.99910 from the or 1. it's the same department of good, bad. Good and bad. Good. Good. So, it's 3 times but I have that 1 minus squared time. Say.

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3% roughly and so the probability of the 3 bits implying that.

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The correcting was translated would be the sum of the point 9, 9, 7 plus 2.0294. so I'm pretty close to 1.

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Now, the probability of the being too bad and the good, which means, we infer the wrong thing.

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That would be it could be bad, bad, good or bad good, bad.

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Or good, bad, bad, and that will be the number. I've got there. C5. 02997 3 bits could be bad with high probability. Point all 1. cute.

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So, at some point, 8, 0T and 9.

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so the probability that we received to bed correctly that c point zero eight point be something to which is the .

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99999 7.

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Around it, so what we do, so and that's.

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Yeah, it's a lot better than the original.

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Correct probability which is point 9 9, 9. so we added.

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You know, 2 more a couple of by tomorrow 0T and Stuart and, um.

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I don't know if I'm right on that. 1 maybe 200. but the point is, this is using probability.

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To get a something that's much.

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You know, to design a hardware circuit, that's much more reliable than the cost was. Of course that.

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Some hardware pest, triple the transmission time. Oops a 2nd, here. Crazy on me.

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Okay, another example of.

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Probably is a test transmission.

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So, Samuel ultimately breeds Morse invented the Telegraph, sending give or take 18.

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40, plus or minus I'm using just instead of running in stops and dashes. You touch the Telegraph key quickly. You get a doc, he touched the Telegraph key. Hold it down a little longer. You get a dash.

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But it's a binary code and use 5 fits for each ladder.

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And that was more steady did this 180 years ago.

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He realized that some English letters are more common than others. A, is very common.

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And it was very rare. So what he did was.

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He was different numbers of dots and dashes for ease and for cues.

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And he would need 1 dot you have to have a little gap, of course, between writers. So the receiver could tell you finishes what the dots and dashes for 1 letter before the next 1 starts when he would be.

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But a cure would be dash. Dash. Dash would be a lot longer.

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So this was a code with reducing probabilities to minimize the.

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To minimize the link to the message.

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Now, why do you care what the link to the message is?

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Well, perhaps your channel is really slow.

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Let me give you an example of a really slow communications channel in history.

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Was the 1st time to see telegraph cable.

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That went from Cornwall, England to Newfoundland.

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Into heart's content Bay. I, I've been there.

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And so this is, I don't give or take 1500 miles long.

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Under sea after the fires had not been invented.

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Tuning and Sarah had not been invented for cables, locked parameters and so on had not been invented.

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So, the cable was seriously.

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Couple did the sea router, which conducts electricity and serious inductance.

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So the transmission was really slow.

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And I think it was less than 1, but a 2nd.

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The basic thing is that at the receiving end.

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The cable is connected to a little coil, a rich.

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Twisted, which caused an electromagnetic.

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Which caused a mirror to rotate slightly and they bounced.

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And being a flight off the mirror and saw, whereas it protected be amended and they could tell how.

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Or was there a voltage going to the cable or not so that this cable was really slow so you'd want to use inefficient.

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Way to transmit text sometimes your channels are slow.

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Okay, now so besides about compression, of course, is that, by the way an expert nurse, Carter is faster than texting. They say.

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You can also get English, you can compress the English text.

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Easily down to 2 bits a ladder and with difficulty that down to 1 bit per ladder if it's normal English that if you're not trying to construct something crazy to break the system. So, because this has so much structure that you can.

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If you take the big streams for 2 separate English paragraphs, and you add them, but I bet you source of all them. But I bet.

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A good cryptography can probably mostly separate those 2 texts, which sounds crazy by looking at correlation. So.

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Any case so, using probability up here.

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For tech up up here for test compression and text compression in the real world.

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I like to give you another example of reliable system design no math and this example.

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And it is real world applications.

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If you might ask you say examples of nuclear power plant, what might cause it to fail.

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Well, if you get a router leak, serious leak.

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And also the operators asleep.

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Friday number of accidents happen in the graveyard shift, and there's a backup pump that the answer is turned off for maintenance.

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Now, you can calculate probability of failure and nuclear Regulatory Commission, in fact, requires things like these be calculated that you combine. You have to think of the probability of things combining and so on.

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But to travelers, so you want to put a backup system and and.

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I actually I got lots of examples here of backup procedures.

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That can cause problems some deadlines around backup thing. It causes.

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Long distance telephone service went down 1 afternoon for a while because.

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There was a C program and code we had a continuous statement wrong and.

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It broke out of the wrong level of loop and the backup procedure said.

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Forced phone calls to go to a backup switch and the backup code wasn't working, right? It caused the failure and that some backup procedures being wrong.

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Okay, so that's just a quick introduction trying to motivate some stuff.

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But I have here, he's talking about this, I decided to write some of this down and also give it.

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A slightly different thing, and this is a summary of what's in the book. So, Here's what I'm thinking of for you, is that if you see.

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The thing described from different points of view, you will understand it better.

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So, you read how to read key watch on professor describes it is very good lecture and you read how.

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00:29:47.038 --> 00:29:50.189
The textbook does it or submarines of that.

210
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A lot of words in the textbook, but it's a lot of information and you see my summaries here and between them, you might start really understanding things.

211
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So, it was a big thing with random experiments and so you got a procedure.

212
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And you're measuring something, so.

213
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For example, procedure might be twice as 1 example coin twice at your experimental procedure.

214
00:30:22.199 --> 00:30:25.558
But now you have to decide, what do you want.

215
00:30:25.558 --> 00:30:32.939
To measure, and maybe you want to measure the number of heads so you tossed the coin twice. There could be several heads.

216
00:30:32.939 --> 00:30:37.798
1 or 2 heads and.

217
00:30:37.798 --> 00:30:44.068
You may want the measurement to be the exact sequence at head.

218
00:30:44.068 --> 00:30:48.118
And tell the hotel.

219
00:30:48.118 --> 00:30:54.838
So, you, the person that designed to experiment says what you want to measure what's interesting to you.

220
00:30:56.068 --> 00:31:02.189
And see all the random experiment. Every time you run it, you make it a different answer.

221
00:31:03.989 --> 00:31:09.778
And we've got some terminology here you got outcome when she.

222
00:31:10.919 --> 00:31:19.348
Price again, it depends how you again, how you choose to define your experiment, but you pass a coin twice.

223
00:31:19.348 --> 00:31:27.209
Your outcome could be the sequence of facts and tails had had telltale would be your for outcomes. Perhaps.

224
00:31:27.209 --> 00:31:31.078
And your password outcomes and.

225
00:31:32.578 --> 00:31:39.179
Now, mathematically, there's different way you might have a finite set of outcomes.

226
00:31:39.179 --> 00:31:46.648
Scale of now, you could have a random experiment, which might have an infinite number of outcomes.

227
00:31:47.818 --> 00:31:52.588
Where can you find Rad case lectures?

228
00:31:53.759 --> 00:31:59.219
Okay, don't go back to the.

229
00:32:02.249 --> 00:32:06.179
Now, or do we have.

230
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I also had the select.

231
00:32:10.169 --> 00:32:13.169
Probability bites.

232
00:32:13.169 --> 00:32:21.419
And he's got 675 of them or something so, and he's made the generally about 10.

233
00:32:21.419 --> 00:32:27.989
10 minutes. Okay. Okay. Next question, what is the seminar for? The.

234
00:32:29.669 --> 00:32:35.159
X a. 2nd, here back.

235
00:32:36.479 --> 00:32:46.318
No, I'm down here and see what they're going to look at the cartoon. Okay some symbol symbol.

236
00:32:49.469 --> 00:32:53.638
That would be a Greek letter.

237
00:32:53.638 --> 00:33:01.199
I think so. Last potential is good. You're saying.

238
00:33:01.199 --> 00:33:05.669
Not so bad so they call into creek sometimes and so.

239
00:33:09.118 --> 00:33:12.838
And.

240
00:33:12.838 --> 00:33:16.769
Yeah. Okay. Okay. So.

241
00:33:16.769 --> 00:33:20.848
Number of outcomes from an experiment, then.

242
00:33:20.848 --> 00:33:29.219
Welcome so it could be finite like Tasha coin 10 times number of heads. It could be countably infinite.

243
00:33:29.219 --> 00:33:39.598
Give an example, I'm going to go to Las Vegas and I'm going to bet read a little.

244
00:33:39.598 --> 00:33:44.548
I'm going to back and tell red comes up on the left. Okay. On.

245
00:33:44.548 --> 00:33:47.969
In might come up on the 1st top, you know.

246
00:33:47.969 --> 00:33:57.778
1st of all, it might come up in a 2nd, and might come up on the 3rd and might take a 1M dollars or whatever. So, let me go back to coins.

247
00:33:57.778 --> 00:34:03.538
Coin these parameters pass the coin. Can I get ahead?

248
00:34:03.538 --> 00:34:06.689
Okay, 50% chance happened on the 1st task.

249
00:34:06.689 --> 00:34:12.509
But it might not 25% change. It happens on the 2nd task. Exactly.

250
00:34:12.509 --> 00:34:15.628
But not in the 1st, not 3rd or later, but the 2nd.

251
00:34:15.628 --> 00:34:20.099
I might take 2, 3 tosses an 8 to the time. It will happen.

252
00:34:20.099 --> 00:34:25.918
On the 3rd toss, so this is it's perfectly well defined experiment.

253
00:34:25.918 --> 00:34:35.759
And but the number of outcomes is infinite 1, 2, 3, 4 or 5 up to any bigger number as you want.

254
00:34:35.759 --> 00:34:43.318
now it's called discrete or countable infinity because i can list the outcomes in order like .

255
00:34:43.318 --> 00:34:56.518
12345 and each 1 has a probability the probability that the 1st head was on the 1st task is 50%. The probability of the 1st head was on the 10th toss would be run in 1 or 2. 4.

256
00:34:57.989 --> 00:35:03.778
An infinite number of outcomes now, but those aren't there's.

257
00:35:03.778 --> 00:35:12.929
that infinite infinity is not as incident as you can get you didn't get a bigger infinity than that and that's called uncountable infinity .

258
00:35:12.929 --> 00:35:18.568
And they, those would be like, 2, real numbers.

259
00:35:18.568 --> 00:35:26.159
That's just a script. R and so maybe my experiment is, I'm going to look at the minimum temperature.

260
00:35:26.159 --> 00:35:37.108
Tonight, and if I recall it's going to be down around 0T Fahrenheit, I think, check what I think tonight or tomorrow night.

261
00:35:37.108 --> 00:35:41.309
Whether that, see.

262
00:35:43.108 --> 00:35:47.338
Saturday night expected mineral minus too.

263
00:35:47.338 --> 00:35:52.498
For people outside the United States that's give or take minus 20.

264
00:35:52.498 --> 00:36:01.079
Sales? Yes. Okay. So our experiment is to look at the temperature temperature, say at 3 0T am.

265
00:36:01.079 --> 00:36:05.039
Well, it's a real number the more accurate. My thermometer.

266
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Than the more digits I'll get and so the outcomes, a real number, it's random, but that's called uncountable.

267
00:36:13.708 --> 00:36:22.829
Because there's actually more real numbers than there are endanger. So, both infinite. But the number of real numbers is bigger.

268
00:36:22.829 --> 00:36:32.159
Then number dangers it's getting beyond this course somewhat. The relevant point to discourse. A very relevant point is.

269
00:36:32.159 --> 00:36:39.599
There are so many reels that the probability of any specific exact real is 0.

270
00:36:39.599 --> 00:36:46.619
i mean it's countable infinity the probability that that coin will get its first head on the fourth toss .

271
00:36:46.619 --> 00:36:50.338
Is 116th, there's an infinite number of.

272
00:36:51.449 --> 00:37:00.958
You know, possible outcomes, any natural number from 1 up, but the probability of these particular number, it's got a probability. It's positive. The problem with the real numbers.

273
00:37:00.958 --> 00:37:08.878
Is that the probability of the temperature being any be exactly any specific? Real number? It is 0.

274
00:37:08.878 --> 00:37:14.759
So you have to do is look at a range. Let's see a question.

275
00:37:15.898 --> 00:37:19.438
Yes, you're ahead of me, Andrew. Exactly.

276
00:37:19.438 --> 00:37:24.298
You have to look at the probability of a range of.

277
00:37:24.298 --> 00:37:30.509
Of numbers, so probably a temperature minimal between minus 5 and 0T or something.

278
00:37:30.509 --> 00:37:36.539
Yeah, and you could I was trying to do it a little more lightly, but yeah, you're ahead of me on that. Thanks.

279
00:37:38.699 --> 00:37:42.719
So so which course covers that here.

280
00:37:42.719 --> 00:37:48.358
Because I never a certain exactly what's covered in which math course, because.

281
00:37:48.358 --> 00:37:52.889
The mass apartment doesn't actually tell us and they also don't actually follow their.

282
00:37:52.889 --> 00:38:00.688
Some of us, so I find out what's actually covered in the other courses by asking you guys.

283
00:38:00.688 --> 00:38:07.588
So, okay, so keep telling me what level of background has already been covered.

284
00:38:07.588 --> 00:38:12.809
But any case, I have to send more detailed box.

285
00:38:12.809 --> 00:38:17.789
Okay, cool.

286
00:38:17.789 --> 00:38:21.449
Okay, I don't 1 brown video.

287
00:38:21.449 --> 00:38:25.170
Heard in Fox and chaos. Okay.

288
00:38:25.170 --> 00:38:29.670
That's cool. They're doing more math and I realized.

289
00:38:31.079 --> 00:38:38.039
So, I can get deeper here so you see most of the points here and 6 but the thing is, maybe some people have not.

290
00:38:38.039 --> 00:38:44.429
Perhaps taken that, so just in case so we got finite sets. Infinite sets accountable or uncountable.

291
00:38:44.429 --> 00:38:53.940
catabolic come that link you can number them 1, 2 3, which you can do for the rationales was a diagonal that's called argument.

292
00:38:53.940 --> 00:38:57.809
Counting rationales.

293
00:39:02.099 --> 00:39:08.429
I'm not accountable and the asportation, George Cantor who discovered this.

294
00:39:08.429 --> 00:39:11.760
You might say that or drove them crazy.

295
00:39:11.760 --> 00:39:17.789
He was in a mental health facility at times, so okay.

296
00:39:17.789 --> 00:39:23.429
So, the probability is, we.

297
00:39:23.429 --> 00:39:26.699
So, the continuous outcomes, all we can do is to assign.

298
00:39:26.699 --> 00:39:33.360
Probabilities to ranges temperature being between minus 5 and 0T or maybe.

299
00:39:33.360 --> 00:39:39.389
And I have an example here, actually with nuclear.

300
00:39:39.389 --> 00:39:50.730
Half lives, and also, you know, what the outcome is, you can say you're looking for real number or you might it. We're just looking for an integer is an example. Here I've got was half lives.

301
00:39:50.730 --> 00:39:55.349
So, I searched around and I, Calvin isotope sodium, 26.

302
00:39:55.349 --> 00:39:58.739
His half life is a 2nd. I shouldn't convenient.

303
00:39:58.739 --> 00:40:05.039
And so an experiment is we make an atom sodium 26. I don't know how you make it from.

304
00:40:05.039 --> 00:40:09.539
Summarize it up to case into it perhaps and.

305
00:40:09.539 --> 00:40:24.090
And the experiment is to watch that Adam, and until it decays now you might see your outcomes a real number the time, which decays or we might say the outcome is the number of complete number of seconds before decays.

306
00:40:24.090 --> 00:40:28.050
So, 1, 2 or 3 and this is countably infinite.

307
00:40:28.050 --> 00:40:31.590
and so the probability of the case in the first second is one half .

308
00:40:31.590 --> 00:40:38.730
the and the second second is a quarter and so on so just like tossing the clients it's the same math .

309
00:40:38.730 --> 00:40:48.000
So, and we can have fun things here that we could you could define whatever outcome you.

310
00:40:49.164 --> 00:41:01.675
You want the probability that it's lifetime is an, even number of seconds, the probability of 0T plus for probably 2 for some probability of 4 and a half. Plus that's the 32nd geometric.

311
00:41:03.480 --> 00:41:07.469
Here each term is a quarter of the previous.

312
00:41:07.469 --> 00:41:15.030
You know, the formula, so probabilities 2 thirds of that lifetime being and they ended your part of the lifetime. You can even number of seconds.

313
00:41:16.739 --> 00:41:25.170
So, and or by the way 1, interesting mathematical thing about the this.

314
00:41:25.170 --> 00:41:35.429
Radioactive decay that the probability of the atom decaying in the next 2nd is independent of how old the atom is.

315
00:41:35.429 --> 00:41:39.030
History doesn't matter. So.

316
00:41:39.030 --> 00:41:46.349
It's called an exponential distribution and we'll study it later. So there are some things I like that.

317
00:41:46.349 --> 00:41:50.460
The probability of success and the next attempt is that.

318
00:41:50.460 --> 00:41:55.380
Does not depend on how many times you've been trying.

319
00:41:56.969 --> 00:42:00.449
Let me take this in 2006. thank.

320
00:42:00.449 --> 00:42:06.179
Again, okay, so now we're going to let the outcome be the real number.

321
00:42:06.179 --> 00:42:10.320
Of the time until it decays counting from when we start the experiment again.

322
00:42:10.320 --> 00:42:15.869
past history doesn't matter the real numbers anything from zero that's your uncountable infinity .

323
00:42:15.869 --> 00:42:21.690
And we can't talk about it being a specific, real number, or you can say the probability that.

324
00:42:21.690 --> 00:42:30.659
It's in some range, and here, the math happens to be the probability that.

325
00:42:30.659 --> 00:42:34.980
The right time is greater than some given numbers 2 to the minus.

326
00:42:34.980 --> 00:42:40.469
That number and then just wait my hands and.

327
00:42:40.469 --> 00:42:43.739
I can derive it if you're out or I can derive it. It's the.

328
00:42:43.739 --> 00:42:48.480
Cover cam was being friendly with Webex.

329
00:42:48.480 --> 00:42:55.050
But by the way you easy, some of this stuff, which totally fails what I'm talking to, you.

330
00:42:55.050 --> 00:42:58.619
It stops, it might have worked earlier. Like, I have an earlier class.

331
00:42:58.619 --> 00:43:07.199
Earlier in the day, that is fewer students Senate, and for some weird reason, this hardware works better when they're if you're.

332
00:43:07.199 --> 00:43:12.690
Members of the people watch and go figure at some Webex that you apparently.

333
00:43:12.690 --> 00:43:18.090
So, I can use a particular hardware configuration, 3 hours ago and it works. I use it.

334
00:43:18.090 --> 00:43:21.449
With you guys that fails. Okay.

335
00:43:21.449 --> 00:43:26.699
Sitting back backwards no. Okay. So we have the thing here.

336
00:43:26.699 --> 00:43:30.239
The 7, 2006 again with the 3rd half life.

337
00:43:30.239 --> 00:43:34.679
And the outcome here is that.

338
00:43:34.679 --> 00:43:39.420
It's a real number so what you can do is, I got point here 9. F.

339
00:43:39.420 --> 00:43:43.500
That the probability that you're going to have to.

340
00:43:43.500 --> 00:43:49.559
Given the half life is a 2nd, that I could derive that thing there. If you're interested in.

341
00:43:49.559 --> 00:43:56.460
Ask, and I could derive it for the next class, but this is a probability that the lifetime theater equal doesn't matter.

342
00:43:56.460 --> 00:44:01.320
Now, given 9, I can calculate the probability of the lifetime.

343
00:44:01.320 --> 00:44:04.380
I'm being in Indiana, so.

344
00:44:04.380 --> 00:44:10.380
That that it decays between 1.23 and 1.24 seconds. I would just subtract the 2.

345
00:44:10.380 --> 00:44:13.380
And I get 3%.

346
00:44:15.210 --> 00:44:27.539
Okay, there's all sorts of stuff here, which may come back to when said, I got all this math. You always got to be asking yourself. That is the math correct?

347
00:44:27.539 --> 00:44:34.949
And so what I'm passing coins, I'm assuming that the coin is fair that 50, 50 each time.

348
00:44:34.949 --> 00:44:40.469
I'm assuming this website you can go and buy funny coins if you are.

349
00:44:40.469 --> 00:44:46.079
I'm assuming that the different.

350
00:44:46.079 --> 00:44:51.780
Don't affect each other for coins. I can't imagine how they would affect each other.

351
00:44:51.780 --> 00:44:55.019
But noise on the communications channel.

352
00:44:55.019 --> 00:45:00.510
Absolutely, they could affect each other because there could be a common cause.

353
00:45:00.510 --> 00:45:04.110
Which causes more errors.

354
00:45:04.110 --> 00:45:07.469
So.

355
00:45:07.469 --> 00:45:14.699
No, that's so effectively you'd be a correlation so you have to send the mass is actually correct.

356
00:45:14.699 --> 00:45:18.059
And I'll have examples of that throughout the course.

357
00:45:18.059 --> 00:45:21.179
Any case back to terminology and again, watch.

358
00:45:21.179 --> 00:45:28.769
Okay, so the individual things you might say, the atoms and the outcomes of the molecules are the events.

359
00:45:28.769 --> 00:45:32.070
And do whatever you want to.

360
00:45:32.070 --> 00:45:41.159
Fine to observe what you want to observe and then we've got set theory, which.

361
00:45:41.159 --> 00:45:48.119
Had in grade school probably I don't know. Maybe I'm seeing Venn diagrams intersection unions.

362
00:45:48.119 --> 00:45:51.389
And you get various axioms for how you combine stuff.

363
00:45:51.389 --> 00:45:57.659
And the Morgan cerumen so on, so you can prove to them.

364
00:45:59.880 --> 00:46:09.449
In different ways, it's a small number of different branches enumerate them list all the possibilities and add them up. That's okay.

365
00:46:09.449 --> 00:46:20.670
Classes of events, when I said like, 2.1.4 I'm kidding you back to a section in the book. So that's the, the book 2.1.4. so.

366
00:46:20.670 --> 00:46:25.920
Set of outcomes as an event we're the only 1 events we can measure.

367
00:46:25.920 --> 00:46:31.170
So, like, intervals for the numbers and so on.

368
00:46:31.170 --> 00:46:45.030
We gotta get those axioms or probability. I'm going to go somewhat light on them while they do create some nice sets of homeworks and exam questions.

369
00:46:45.030 --> 00:46:51.539
He talks about that, I think it's and lecture 3 or something.

370
00:46:51.539 --> 00:46:59.730
And so they're just common sense things about what our probabilities have and.

371
00:46:59.730 --> 00:47:09.389
If we find the reason mathematicians do, this is if we can find these general rules, then we can start proving things and they apply to.

372
00:47:09.389 --> 00:47:14.309
Everywhere so probabilities we assume they're from 0T to 1.

373
00:47:14.309 --> 00:47:18.659
And so.

374
00:47:18.659 --> 00:47:24.750
Some of the various actually, actually, it's not negative. It's 0T or axiom.

375
00:47:24.750 --> 00:47:32.909
2, I says that says, like, the set of everything and the probability of something happening.

376
00:47:32.909 --> 00:47:40.590
If anything that happening is 1, and then 3, here, I, these start getting something important.

377
00:47:41.909 --> 00:47:45.780
Are we supposed to have on.

378
00:47:46.889 --> 00:47:56.519
I was thinking that people had that Andrew, but if you don't tell me and I'll spend more time on it, not at all.

379
00:47:56.519 --> 00:48:01.440
Thank you trust and okay. I will spend more time on that.

380
00:48:01.440 --> 00:48:12.090
So, let me actually do a little now. Ok, I don't trust myself.

381
00:48:12.090 --> 00:48:19.559
Putting the over camera on so I'll try with some drawing program and see.

382
00:48:19.559 --> 00:48:22.559
And.

383
00:48:25.800 --> 00:48:31.530
Okay.

384
00:48:32.760 --> 00:48:38.369
Okay, here works.

385
00:48:40.675 --> 00:48:54.175
I'm not, I don't have a touchscreen on this computer, but we'll see. So, basically you've got things like this. I'll use the cards as an example. So we've got things here. Like, that's.

386
00:48:55.170 --> 00:48:59.789
And let's say.

387
00:49:01.110 --> 00:49:05.489
So.

388
00:49:05.489 --> 00:49:10.590
Okay, so okay.

389
00:49:10.590 --> 00:49:14.369
Bigger so you can read it actually.

390
00:49:14.369 --> 00:49:18.300
Silence.

391
00:49:18.300 --> 00:49:22.619
Silence.

392
00:49:22.619 --> 00:49:26.219
Okay, so basically.

393
00:49:26.219 --> 00:49:29.610
Silence.

394
00:49:31.170 --> 00:49:36.210
A deck of cards. Okay. And, um.

395
00:49:38.460 --> 00:49:41.550
Silence.

396
00:49:41.550 --> 00:49:47.309
Hello.

397
00:49:48.510 --> 00:49:52.980
Playing cards. Okay.

398
00:49:52.980 --> 00:49:56.400
Silence.

399
00:49:56.400 --> 00:50:02.639
Silence.

400
00:50:02.639 --> 00:50:09.780
Okay, okay. So so we can talk about things. Okay.

401
00:50:09.780 --> 00:50:12.960
We're going to call this.

402
00:50:12.960 --> 00:50:24.000
I'll call this a crisis. Okay so now you can start doing thinking is a profitability of the card as a queen is 1 quarter. Okay.

403
00:50:24.000 --> 00:50:27.210
The card as an ace is.

404
00:50:27.210 --> 00:50:32.190
1 SEC. Okay.

405
00:50:32.190 --> 00:50:38.489
And then inside here called this X.

406
00:50:38.489 --> 00:50:44.550
Silence.

407
00:50:44.550 --> 00:50:47.639
Silence.

408
00:50:47.639 --> 00:50:57.269
There is 1 card. Okay. And I can talk about probability of access.

409
00:50:57.269 --> 00:51:01.469
152 okay, so now, the thing is that.

410
00:51:01.469 --> 00:51:05.969
Is the set of.

411
00:51:05.969 --> 00:51:10.139
Green cards. Okay.

412
00:51:10.139 --> 00:51:13.679
A s, the set of.

413
00:51:13.679 --> 00:51:21.090
A scarred. Okay. So now, what I can do is I can intersect 2 sets and.

414
00:51:21.090 --> 00:51:26.699
Hello.

415
00:51:28.110 --> 00:51:33.960
Silence.

416
00:51:36.389 --> 00:51:41.579
Jason.

417
00:51:44.730 --> 00:51:48.329
Silence.

418
00:51:48.329 --> 00:51:51.900
Oh, it's not letting me do it.

419
00:51:53.909 --> 00:51:57.449
Thank you.

420
00:51:57.449 --> 00:52:04.500
Hello hey.

421
00:52:06.389 --> 00:52:11.880
2 sets. Okay.

422
00:52:13.050 --> 00:52:17.130
I would do it. Okay.

423
00:52:17.130 --> 00:52:21.449
To.

424
00:52:21.449 --> 00:52:27.719
Okay, so that's really a notation and, um.

425
00:52:27.719 --> 00:52:33.869
So, now we can talk about the probability of say Q.

426
00:52:33.869 --> 00:52:38.159
Hey, that's called Union.

427
00:52:38.159 --> 00:52:51.869
That's going to be, you see 152 and a well, now, this is interesting. Now, we get to some mass, the probability of Q, but.

428
00:52:51.869 --> 00:52:58.409
Plus the probability of a minus the probability of.

429
00:52:58.409 --> 00:53:02.130
To intersect a.

430
00:53:02.130 --> 00:53:10.469
1, 2, plus 1.

431
00:53:10.469 --> 00:53:14.099
Minus.

432
00:53:14.099 --> 00:53:18.239
152 so a chromosome.

433
00:53:18.239 --> 00:53:24.059
Do so 2 plus.

434
00:53:24.059 --> 00:53:30.480
It's 171652 if I got it right?

435
00:53:30.480 --> 00:53:36.059
So this is set today. Okay, this is going.

436
00:53:37.079 --> 00:53:41.519
Silence.

437
00:53:41.519 --> 00:53:49.530
Okay, so you've got your take on intersections and so on.

438
00:53:49.530 --> 00:53:54.690
Silence.

439
00:53:56.369 --> 00:54:00.750
Okay.

440
00:54:02.400 --> 00:54:06.300
Silence.

441
00:54:06.300 --> 00:54:10.559
Silence.

442
00:54:10.559 --> 00:54:14.730
Silence.

443
00:54:14.730 --> 00:54:23.699
He says I'm in Queens and not Asus.

444
00:54:25.469 --> 00:54:29.039
Silence.

445
00:54:29.039 --> 00:54:33.150
Right.

446
00:54:34.349 --> 00:54:37.619
Silence.

447
00:54:37.619 --> 00:54:40.920
Okay, I know.

448
00:54:43.469 --> 00:54:50.340
Okay, 13 to learn and he says.

449
00:54:50.340 --> 00:54:54.480
And.

450
00:54:54.480 --> 00:54:59.760
That's better. Okay. Clearly our hearts and.

451
00:55:13.590 --> 00:55:18.750
Okay.

452
00:55:18.750 --> 00:55:22.469
Somebody was awake.

453
00:55:22.469 --> 00:55:26.309
Silence.

454
00:55:26.309 --> 00:55:33.119
Silence.

455
00:55:33.119 --> 00:55:36.750
Okay.

456
00:55:36.750 --> 00:55:40.349
Silence.

457
00:55:40.349 --> 00:55:44.369
Okay, so.

458
00:55:44.369 --> 00:55:48.239
In any case.

459
00:55:48.239 --> 00:55:53.519
I don't play cards. Okay so.

460
00:55:54.960 --> 00:55:59.070
Quarter of them are hard to 13th of them are a says.

461
00:55:59.070 --> 00:56:02.699
So this would be.

462
00:56:03.840 --> 00:56:07.800
Instead of Q, we could have H, but I'm not going to rewrite them all.

463
00:56:07.800 --> 00:56:16.260
We'll need algebra and Secretary. Okay you've got unions you've got intersections. He got sets and so on.

464
00:56:16.260 --> 00:56:22.079
Um, and right.

465
00:56:22.079 --> 00:56:26.340
Yeah, and you get this thing up here. Okay.

466
00:56:27.809 --> 00:56:30.989
And you could get even on.

467
00:56:32.190 --> 00:56:36.239
You know, you could get even pants here, but okay.

468
00:56:37.289 --> 00:56:42.449
I'll try to save that thing and put it up and.

469
00:56:42.449 --> 00:56:49.019
Okay, so we get things like this here.

470
00:56:49.019 --> 00:56:59.730
Probability of there being a queen is not negative probability of any card at all is 1 and okay. Let's take the hearts.

471
00:56:59.730 --> 00:57:12.659
So so they discharged the same card is not 1st, a heart and an ace. So probability of heart always the probability of the hard plus the probability of an ace. Okay.

472
00:57:12.659 --> 00:57:16.769
And then you could have more than.

473
00:57:16.769 --> 00:57:23.909
Possible events here and get a general rule there.

474
00:57:23.909 --> 00:57:29.340
Okay, okay Here's what I have a queen and a heart. That's what I had forgotten.

475
00:57:29.340 --> 00:57:33.059
Okay, courageous arcades hard queen and heart.

476
00:57:33.059 --> 00:57:37.590
They can intersect, so we get this thing here. Okay.

477
00:57:37.590 --> 00:57:43.380
So, the problem that being a queen, all our heart, we add the 2 of them, we have to subtract the overlap.

478
00:57:43.380 --> 00:57:46.980
Okay, 16 here I've got the destroying.

479
00:57:46.980 --> 00:57:51.960
Clubs and hearts.

480
00:57:51.960 --> 00:57:55.530
So, 17 here I got to flip the fair coin.

481
00:57:55.530 --> 00:58:02.610
So, the event that you see had the 1st time, the ice flip.

482
00:58:02.610 --> 00:58:09.150
And the problem even have an exact step is 1 or 2 to the I just joined so I could count.

483
00:58:09.150 --> 00:58:16.980
The budget of course, the 10th or later toss is that that's a geometric series. So you could easily add it up.

484
00:58:16.980 --> 00:58:26.010
Okay, by the way for stuff like this package is like mathematical I could do that also for you.

485
00:58:26.010 --> 00:58:38.909
Now, we got a little Super skipped Siemens to compliment. So, is that the card is a queen then a compliment is of the cards. The other 12 cases.

486
00:58:38.909 --> 00:58:47.429
Her heart versus not hard. Okay. And then a chlorine is a minor so probably some advantage.

487
00:58:47.429 --> 00:58:53.130
Circle to run and probably get all happen. That's or what's attached to it is 0.

488
00:58:53.130 --> 00:58:56.639
And we can do probability of.

489
00:58:56.639 --> 00:59:06.090
We could start getting probabilities and things like a 21, 8 here assumes all the events I just joined.

490
00:59:06.090 --> 00:59:18.179
So, you know, clubs and whatever the problem with them is the center of the profitability. So probably of hearts or clubs together is that it's a quarter for each. So that's a half.

491
00:59:18.179 --> 00:59:24.059
And then tomorrow is not going to write it down. It involves.

492
00:59:24.059 --> 00:59:28.920
Any characters, but 5 is approximately it here.

493
00:59:28.920 --> 00:59:32.760
So, in that.

494
00:59:34.289 --> 00:59:37.710
So, there's someone you mathematics probability.

495
00:59:37.710 --> 00:59:43.230
And said we're going to assume it in various cases here.

496
00:59:45.960 --> 00:59:53.760
Yeah, thank you Andrew. Ok, so it converts into an intersection when.

497
00:59:53.760 --> 00:59:58.230
For the compliment and distribution law sort of, thank you.

498
00:59:58.230 --> 01:00:05.639
Okay, no, you get some questions.

499
01:00:05.639 --> 01:00:12.510
What I'll do is, I'll let you think about that so anyone you can chime in and.

500
01:00:14.610 --> 01:00:21.420
So, in the event, a uniform probability distribution here on 0T to 1.

501
01:00:21.420 --> 01:00:26.519
A, is some point to 2.6. so does anyone type in what's the probability of a.

502
01:00:29.670 --> 01:00:33.539
This isn't graded so just if you.

503
01:00:34.650 --> 01:00:37.949
Want to try then.

504
01:00:43.260 --> 01:00:47.400
For us to do, do you think he's right or wrong?

505
01:00:49.889 --> 01:00:52.889
Right, yeah, I agree with you.

506
01:00:52.889 --> 01:00:59.610
Good okay. Format. What's the probability of fee here that goes from? Point? 4 off to run.

507
01:01:02.070 --> 01:01:10.050
1 6? Yes. Okay. It looks right now what about the union of a and B, what's the probability of that?

508
01:01:10.050 --> 01:01:17.099
Let me scroll back up on so you can see a, and B, what's the proper the you have the 2.

509
01:01:19.559 --> 01:01:25.500
Yep. Okay good. And the probability of the intersection.

510
01:01:25.500 --> 01:01:30.360
I'll be there and be up probability of a intersect point. 2.

511
01:01:30.360 --> 01:01:34.650
Good so, probably, they plus probably to be.

512
01:01:34.650 --> 01:01:40.050
My, my let's say you're in, gives the intersection and so on so.

513
01:01:40.050 --> 01:01:43.289
Human press intersection equals the 2 added separately.

514
01:01:43.289 --> 01:01:48.539
Cool.

515
01:01:48.539 --> 01:01:52.260
Compliment.

516
01:01:52.260 --> 01:01:55.980
Oh, I got the answers. Yeah.

517
01:01:59.280 --> 01:02:02.760
I just supply roll to.

518
01:02:02.760 --> 01:02:14.670
So, I'm going to if I have a primarily distribution at some point.

519
01:02:14.670 --> 01:02:19.380
I have to define it for you and I defined it in role too. So.

520
01:02:19.380 --> 01:02:24.389
All the questions for a, and B, I just plugged in and.

521
01:02:24.389 --> 01:02:34.079
For a union B phase point, 2, 2.6 and base point 4 to run the urine and just look at that. That's going to be point 2 to run.

522
01:02:34.079 --> 01:02:39.239
And so the probability of this, from point 2 to 1 is 1 minus point 2.8.

523
01:02:39.239 --> 01:02:46.349
In a section of 2.6.42.1, the intersection is going to be point 4. 2.6.

524
01:02:46.349 --> 01:02:51.449
And probably, that's point 6 minus point 4.

525
01:02:51.449 --> 01:02:55.170
So That'll be fine. So.

526
01:02:56.219 --> 01:03:00.269
I could draw figure for that if you want me to, but.

527
01:03:00.269 --> 01:03:03.300
Compliment and that's.

528
01:03:05.340 --> 01:03:10.590
You know, I could draw a little figure.

529
01:03:13.199 --> 01:03:16.349
Silence.

530
01:03:16.349 --> 01:03:21.480
Silence.

531
01:03:23.519 --> 01:03:27.659
Sure.

532
01:03:31.230 --> 01:03:36.719
Okay, so while we have here is.

533
01:03:37.860 --> 01:03:41.309
Chile.

534
01:03:41.309 --> 01:03:48.539
Okay, so that we got here, let's say a.

535
01:03:52.289 --> 01:03:57.719
You know, and whatever.

536
01:03:57.719 --> 01:04:01.019
Going to.

537
01:04:04.769 --> 01:04:08.730
Silence.

538
01:04:08.730 --> 01:04:15.719
Okay, so now a is point 2.6.

539
01:04:21.900 --> 01:04:27.570
This is a.

540
01:04:27.570 --> 01:04:30.780
Okay.

541
01:04:30.780 --> 01:04:36.239
B is point 4.

542
01:04:38.309 --> 01:04:42.750
Silence.

543
01:04:44.070 --> 01:04:48.750
Huge.

544
01:04:48.750 --> 01:04:53.309
Silence.

545
01:04:53.309 --> 01:04:58.199
Kind of prostrate.

546
01:04:58.199 --> 01:05:03.119
Okay, so.

547
01:05:05.039 --> 01:05:12.210
So a intersect B.

548
01:05:12.210 --> 01:05:16.530
That's going to be here.

549
01:05:17.579 --> 01:05:22.320
Okay.

550
01:05:23.670 --> 01:05:28.860
Okay.

551
01:05:28.860 --> 01:05:34.289
And B is going to be.

552
01:05:35.670 --> 01:05:39.090
Silence.

553
01:05:39.090 --> 01:05:42.449
Silence.

554
01:05:44.369 --> 01:05:50.489
Silence.

555
01:05:50.489 --> 01:06:00.300
Okay, so the intersection is a part of the line where they're both. True. The union is a part of the line where either is true.

556
01:06:00.300 --> 01:06:07.320
Silence.

557
01:06:07.320 --> 01:06:11.820
A.

558
01:06:11.820 --> 01:06:19.170
Because this time, because I said over here.

559
01:06:19.170 --> 01:06:23.849
That's the priority.

560
01:06:23.849 --> 01:06:26.940
Some other help from a, to be was be minus say.

561
01:06:26.940 --> 01:06:31.739
It's a definition so.

562
01:06:31.739 --> 01:06:35.789
Here are the probably just aligned to the line stuff.

563
01:06:35.789 --> 01:06:40.230
Okay.

564
01:06:40.230 --> 01:06:45.840
And then 1, other thing, the compliment.

565
01:06:45.840 --> 01:06:51.719
Whoops, running out of paper here about the.

566
01:06:54.210 --> 01:06:58.949
In between here.

567
01:07:01.409 --> 01:07:05.969
A C, the conference.

568
01:07:05.969 --> 01:07:09.719
That's going to be a kind of color.

569
01:07:09.719 --> 01:07:13.320
And see, it.

570
01:07:13.320 --> 01:07:20.039
That was confident there just a 2nd.

571
01:07:20.039 --> 01:07:24.210
Silence.

572
01:07:24.210 --> 01:07:29.099
Okay.

573
01:07:29.099 --> 01:07:38.550
Same f***, new color, dark green. So the compliment is a part of the line. It's not a, and it's going to be this.

574
01:07:38.550 --> 01:07:43.079
Plus this.

575
01:07:43.079 --> 01:07:49.079
2 parts here, so it's a part that's not a.

576
01:07:49.079 --> 01:07:53.579
So, the compliment for the.

577
01:07:55.889 --> 01:07:59.940
Be say the compliment is.

578
01:07:59.940 --> 01:08:03.869
And she was grad.

579
01:08:03.869 --> 01:08:11.730
The compliment is what's not be and that's from here over to here.

580
01:08:11.730 --> 01:08:17.310
So, on.

581
01:08:17.310 --> 01:08:20.789
They were events.

582
01:08:23.130 --> 01:08:26.130
No, the event is a range here.

583
01:08:30.810 --> 01:08:34.590
Silence.

584
01:08:34.590 --> 01:08:38.100
Silence.

585
01:08:38.100 --> 01:08:43.170
Silence.

586
01:08:43.170 --> 01:08:48.510
Silence.

587
01:08:48.510 --> 01:08:52.829
So.

588
01:08:52.829 --> 01:08:55.859
Okay.

589
01:08:57.659 --> 01:09:01.890
Okay, that comes back to.

590
01:09:01.890 --> 01:09:07.710
Real numbers, so.

591
01:09:09.449 --> 01:09:17.880
Then you can do combo things um.

592
01:09:17.880 --> 01:09:21.090
I also have an example here. Um.

593
01:09:21.090 --> 01:09:24.210
Transmission several times.

594
01:09:24.210 --> 01:09:29.250
But I really don't let you think about this, or I'll work on this on.

595
01:09:29.250 --> 01:09:32.430
Monday, I think so.

596
01:09:32.430 --> 01:09:35.939
Let me well, let me just review.

597
01:09:35.939 --> 01:09:42.000
For just a few minutes what we were doing.

598
01:09:42.000 --> 01:09:45.119
1st, we got the files up here, which I'll try to.

599
01:09:45.119 --> 01:09:50.279
And so if I can, they don't always work.

600
01:09:50.279 --> 01:09:54.659
And.

601
01:09:54.659 --> 01:09:59.159
Yeah, so so I have some examples here probability.

602
01:09:59.159 --> 01:10:03.510
Silence.

603
01:10:03.510 --> 01:10:09.960
Okay, awesome. Okay. Thanks for reminding me.

604
01:10:12.180 --> 01:10:15.510
Silence.

605
01:10:15.510 --> 01:10:23.819
Okay, so got real examples of probability here. Noisy channels.

606
01:10:23.819 --> 01:10:28.260
Compression generally reliable things. People.

607
01:10:28.260 --> 01:10:39.060
Like I said, the government regulators will require things like this to be estimated whether the estimates are correct is beyond this course.

608
01:10:39.060 --> 01:10:43.949
Here we got random experiments of procedure plus measurements.

609
01:10:43.949 --> 01:10:52.949
So you got your atoms that are specific observation then they group up into events and we get various.

610
01:10:52.949 --> 01:11:04.260
This is irrelevant back to us. And the point is, you've got some experiments of the set of outcomes is finite.

611
01:11:04.260 --> 01:11:07.529
Clients heads or tails of dies 1 through 6.

612
01:11:07.529 --> 01:11:11.430
Um, so.

613
01:11:11.430 --> 01:11:20.699
And sometimes it's countably infinite number of tosses. Still the coin comes up heads, or it could be uncomfortably independent like, temperature tonight.

614
01:11:36.569 --> 01:11:45.060
Something and just some examples here of countably infinite and so on.

615
01:11:46.260 --> 01:11:56.369
They need to do and we've got some mass involving sets. So thing is also look at Iraqis video and talks about this nicely.

616
01:11:56.369 --> 01:12:00.270
And some general act seems about probability and I use.

617
01:12:00.270 --> 01:12:06.390
Mangled the example of that there I'll try to include again that.

618
01:12:06.390 --> 01:12:09.720
Thing that I handwrite and use the program doesn't crash on me.

619
01:12:09.720 --> 01:12:13.710
And probably, so we're continuing on.

620
01:12:14.760 --> 01:12:21.090
Read some guys say I look at rich case.

621
01:12:21.090 --> 01:12:28.350
So, he actually emphasizes bite number 3 and gets into sample spaces for and we'll start talking about next time.

622
01:12:28.350 --> 01:12:33.180
And have some fun.

623
01:12:33.180 --> 01:12:36.930
Jelly beans cause acne.

624
01:12:37.614 --> 01:12:40.465
Convention, I may look at the 5% chance that the experiment was wrong.

625
01:12:40.465 --> 01:12:53.095
So being said, in blue jelly being killed Jelly, being steady, 20, jelly beans later, green, jelly beans did at the 5% level. So.

626
01:12:54.090 --> 01:12:57.569
Okay, 95 yeah. Okay.

627
01:12:59.579 --> 01:13:04.890
I don't understand.

628
01:13:07.619 --> 01:13:10.949
What do you mean? The parallel in particular.

629
01:13:18.569 --> 01:13:26.220
The size of the set well, it could be either. It could be countably unfinished. It could be continuously infinite.

630
01:13:34.170 --> 01:13:38.369
Oh, okay. I'm still.

631
01:13:41.699 --> 01:13:48.960
Oh, I'm sorry, where is this?

632
01:13:48.960 --> 01:13:55.260
Silence.

633
01:13:55.260 --> 01:13:58.649
Silence.

634
01:13:58.649 --> 01:14:02.100
Silence.

635
01:14:03.300 --> 01:14:06.510
Where did I put it on?

636
01:14:08.369 --> 01:14:12.659
Okay.

637
01:14:12.659 --> 01:14:21.569
Silence.

638
01:14:21.569 --> 01:14:29.819
Oh, okay. Thank you. Vertical bars. Mean the size the measure.

639
01:14:29.819 --> 01:14:35.340
Silence.

640
01:14:35.340 --> 01:14:40.680
Silence.

641
01:14:40.680 --> 01:14:43.680
Silence.

642
01:14:43.680 --> 01:14:49.380
Silence.

643
01:14:49.380 --> 01:14:53.789
Silence.

644
01:14:53.789 --> 01:14:56.789
Silence.

645
01:14:56.789 --> 01:15:02.279
Silence.

646
01:15:02.279 --> 01:15:05.520
Silence.

647
01:15:07.229 --> 01:15:10.560
Silence.

648
01:15:10.560 --> 01:15:17.640
Silence.

649
01:15:18.989 --> 01:15:23.430
Silence.

650
01:15:23.430 --> 01:15:26.909
Silence.

651
01:15:26.909 --> 01:15:30.569
Silence.

652
01:15:30.569 --> 01:15:34.170
Silence.

653
01:15:34.170 --> 01:15:46.890
Silence.

654
01:15:46.890 --> 01:16:01.229
Silence.

655
01:16:01.229 --> 01:16:07.079
Okay, have a good weekend.

656
01:16:07.079 --> 01:16:13.739
I'll stay here a few minutes in case those questions.

657
01:16:21.689 --> 01:16:29.939
Professor, I actually have questions about back with the 3 bits arriving. Correct back in.

658
01:16:29.939 --> 01:16:33.869
Silence.

659
01:16:33.869 --> 01:16:40.590
Silence.

660
01:16:40.590 --> 01:16:44.550
Silence.

661
01:16:44.550 --> 01:16:49.170
Silence.

662
01:16:49.170 --> 01:16:58.289
Silence.

663
01:16:58.289 --> 01:17:01.619
Silence.

664
01:17:01.619 --> 01:17:05.699
Silence.

665
01:17:05.699 --> 01:17:09.539
Silence.

666
01:17:09.539 --> 01:17:13.380
Silence.

667
01:17:13.380 --> 01:17:17.039
Silence.

668
01:17:17.039 --> 01:17:20.850
Silence.

669
01:17:20.850 --> 01:17:25.409
Silence.

670
01:17:25.409 --> 01:17:30.720
Silence.

671
01:17:30.720 --> 01:17:33.899
Silence.

672
01:17:33.899 --> 01:17:39.689
Silence.

673
01:17:39.689 --> 01:17:43.109
Silence.

674
01:17:43.109 --> 01:17:48.899
Silence.

675
01:17:50.010 --> 01:17:53.670
Silence.

676
01:17:53.670 --> 01:17:57.359
Silence.

677
01:17:58.920 --> 01:18:04.979
Silence.

678
01:18:04.979 --> 01:18:08.489
Silence.

679
01:18:08.489 --> 01:18:14.729
Silence.

680
01:18:14.729 --> 01:18:18.270
Silence.

681
01:18:18.270 --> 01:18:21.840
Silence.

682
01:18:21.840 --> 01:18:25.979
Silence.

683
01:18:25.979 --> 01:18:29.369
Silence.

684
01:18:29.369 --> 01:18:33.420
Silence.

685
01:18:33.420 --> 01:18:38.189
Silence.