WEBVTT 1 00:02:02.310 --> 00:02:05.400 Hello. 2 00:02:05.400 --> 00:02:10.199 Okay, good, good afternoon. 3 00:02:10.199 --> 00:02:13.560 So. 4 00:02:13.560 --> 00:02:18.990 Profitability class 3 and I'm getting a funny echo. 5 00:02:18.990 --> 00:02:19.944 Just a 2nd 6 00:03:08.365 --> 00:03:10.705 probability class 3. 7 00:03:11.310 --> 00:03:17.009 And now we can actually. 8 00:03:19.979 --> 00:03:24.000 I'll get to the question, and as soon as I can figure out what's going on here. 9 00:03:34.259 --> 00:03:38.909 Okay, I'm trying to share my screen. I'm having some problems, but. 10 00:03:38.909 --> 00:03:49.050 Let's see. Can you hear me. 11 00:03:49.050 --> 00:03:56.969 I'm good, thank you. Okay, so. 12 00:03:56.969 --> 00:04:01.229 Last 3, what was the question from the text book? 13 00:04:01.229 --> 00:04:04.229 Somebody had a question about the textbook reading. 14 00:04:05.849 --> 00:04:13.409 So well, when you think of the question, you can. 15 00:04:13.409 --> 00:04:24.870 Ask later, so well, the textbook is to follow on with what I'm talking about. I put the main points. 16 00:04:24.870 --> 00:04:30.538 On on the blog, so the textbook is to give another perspective together with. 17 00:04:30.538 --> 00:04:41.129 Retried key, because my feeling is that if you see the same idea, presented in a couple of different ways, then. 18 00:04:41.129 --> 00:04:47.309 You are more likely to understand it. That's my point. Also. You got to check some of the textbook to. 19 00:04:48.329 --> 00:04:57.298 To answer the homework question, but the main points I will have on the on my blog. So. 20 00:04:58.559 --> 00:05:01.678 Okay, so. 21 00:05:03.778 --> 00:05:16.319 1st, before we get started, I'm just curious since we got the storm starting where are people now like, I'm and I'm 10 miles west of I can look out my window and I see very light snow, just starting. 22 00:05:16.319 --> 00:05:22.528 Where are the rest of you? Like? Some people are in China so you're not seeing the storm Troy. Okay. 23 00:05:22.528 --> 00:05:31.468 You get the sorry later tonight anyone down South so, I guess New York City it'll watsco Harry Hudson Valley. Oh, okay. 24 00:05:31.468 --> 00:05:41.519 So, all going to see the storm about the same time that's an advantage of being online. Um, by the way I have a Tesla. 25 00:05:41.519 --> 00:05:47.668 Long Island. Okay. Hope you stock in some food. Okay. 26 00:05:47.668 --> 00:05:51.718 New Jersey. Okay. 27 00:05:51.718 --> 00:06:00.509 In a chance if I winter camping, now I've actually got a Tesla, um, power to test the power walls installed. 28 00:06:00.509 --> 00:06:10.408 6 inches in duchess. Cool. So I've got Tesla power wall installed in the house. And the theory is that I have about, um. 29 00:06:10.408 --> 00:06:18.598 26 kilowatt hours of batteries down in the garage so I can run in the house for. 30 00:06:18.598 --> 00:06:21.899 Uh, you know, I, I could run without power for a day or so. 31 00:06:21.899 --> 00:06:26.488 Um, so I've just tested we had a half hour blackout. 32 00:06:26.488 --> 00:06:34.673 In December and it worked for today. It's basically I bought it because it's a toy. I like toys in departments. So, electrical toys are relevant. 33 00:06:35.064 --> 00:06:42.713 I also have a kilowatts of solar panels on the roof, but of course, being in the winter, and they're not connected. Right? Yet, but. 34 00:06:43.019 --> 00:06:47.548 That's the cool thing with the big batteries in the garage. 35 00:06:47.548 --> 00:06:53.218 Do the power walls of grid tie convert here as soon as it is switch over. 36 00:06:55.043 --> 00:07:05.153 And burgers, I'm not certain what you mean by a grid tie inverter, but it's charged from the grid and currently discharged from the grid and discharges to the house. 37 00:07:05.363 --> 00:07:14.903 Unfortunately, when it switches over when the house switches over from the grid to the power walls, I can get a blip for a fraction of a 2nd, sometimes. 38 00:07:15.178 --> 00:07:28.769 No, it happens automatically. There's no transfer switch. I switch it all happened. All things. All computerized could also connected to the mothership. So test I ever get a major software issue and. 39 00:07:28.769 --> 00:07:40.079 You know, the quote, Elon Musk, every test, the car in the country might head to the Rhode Island, which would annoy Rhode Island. Everything could go dead but though it switches over automatically and. 40 00:07:40.079 --> 00:07:48.269 There's a blip of a fraction of a 2nd, sometimes. So I've got 1 of these, you know, 10 dollar o'clock watches. You get it. 41 00:07:48.744 --> 00:07:57.024 Radio is you get at Wal, Mart, and it reset itself. The book was so short, but of course laptops have no problem, because they got batteries. 42 00:07:57.384 --> 00:08:11.423 The other thing is, the power wall, it fully charged itself a day ago when it gets a notice that there's a storm coming in it fully charges itself. Otherwise it stays sort of like app charged. Now if I ever get the. 43 00:08:12.329 --> 00:08:20.848 Solar panels working properly grumble, grumble, grumble, solar edge. Then the idea is that the. 44 00:08:20.848 --> 00:08:32.639 Solar panels charge into the power walls and then I, then I met meter and over the course of a year I'm going to about break even so. 45 00:08:32.639 --> 00:08:40.798 You know, on hot summer days, it'll generate electricity, charge the power wall batteries and then feed it to the grid on cold winter nights. It well. 46 00:08:40.798 --> 00:08:44.219 Discharge so that's the cool thing. 47 00:08:45.778 --> 00:08:53.278 Or, you know, resetting a 5 dollar 10 dollar clock doesn't take a very large flip. Well, it consumption to below the solar. 48 00:08:53.278 --> 00:09:00.629 Yes, the idea. Well, 1st, if I'm not consuming much and so. 49 00:09:00.629 --> 00:09:05.188 The solar panels, theoretically total 8 kilowatts. 50 00:09:05.188 --> 00:09:12.149 And so if I'm say consuming maybe a kilowatt, perhaps then. 51 00:09:13.769 --> 00:09:20.788 Then it will charge the power wall and then feed the rest into the grid. And I have a new meter installed. 52 00:09:20.788 --> 00:09:29.759 Which can run backwards so, and then it basically it nets out at the end of the year. Well. 53 00:09:29.759 --> 00:09:38.578 Basically, I pay them or they pay me. The thing is, at the end of the year, what they pay me is less per kilowatt hour than what I paid them. But, hey, it's cool. 54 00:09:38.578 --> 00:09:42.568 Um, so. 55 00:09:42.568 --> 00:09:49.499 No fun toys and I can actually look right now, I run an app on my phone and I can see. 56 00:09:49.499 --> 00:09:57.958 Um, that I am. 57 00:09:59.158 --> 00:10:03.359 1.1 kilowatts um, let's see if this works. 58 00:10:09.538 --> 00:10:14.038 1, there we go. 1.2 kilowatts. 59 00:10:14.038 --> 00:10:19.798 I'm going from the grid to the house and is a storm watch thing and. 60 00:10:19.798 --> 00:10:27.688 And this would show power flow to and from the solar panels, and the power wall battery, if that was actually working, right? 61 00:10:27.688 --> 00:10:32.009 So, okay. 62 00:10:32.009 --> 00:10:38.668 Now, you're actually paying our Pi to learn about probability. 63 00:10:38.668 --> 00:10:42.089 So, I see. 64 00:10:42.089 --> 00:10:45.599 I can get sharing working, right? 65 00:10:45.599 --> 00:10:50.458 Try this again. 66 00:10:50.458 --> 00:10:56.219 Share you get the screen sharing with black. 67 00:10:56.219 --> 00:11:02.519 Wow, technology from time to time works. 68 00:11:02.519 --> 00:11:07.019 Always such a pleasant surprise at a. 69 00:11:07.019 --> 00:11:21.568 Homework 2, I hadn't realized that you use great scope as a way to list all your due date. So I'm going to put it up on grade scope tonight. I think so. Okay. Real World probability. 70 00:11:21.568 --> 00:11:26.458 Massachusetts has a lottery and. 71 00:11:26.458 --> 00:11:41.423 No, I've actually don't play the lottery much. Well, I got to tell you my sure. Fire away every year in New York state. I actually clear 1 or 200 dollars more than the average New Yorker tax free on the state lotteries. 72 00:11:42.418 --> 00:11:55.649 Guess how I do it guaranteed what you could do it yourself you could make 1 or 200 dollars more than the average New Yorker on the state lottery tax free. 73 00:11:57.058 --> 00:12:01.528 Any ideas how you do it? That's it. 74 00:12:01.528 --> 00:12:05.908 Okay, you got it, so. 75 00:12:05.908 --> 00:12:10.048 Okay, but some MIT students, um. 76 00:12:10.048 --> 00:12:13.288 Status chose so. 77 00:12:13.288 --> 00:12:19.678 So the thing with the lottery, normally, the expectation all define it for you later. 78 00:12:19.678 --> 00:12:29.308 But it's how much on the average you're going to win or lose. And the thing is the Massachusetts state lottery. 79 00:12:29.308 --> 00:12:36.989 A couple of times a year, the expectation would go positive because if no 1 won, the big prize would roll over. 80 00:12:36.989 --> 00:12:44.879 It would roll over to the next drawing, which we another 2 weeks or something. So but the thing is. 81 00:12:45.474 --> 00:12:56.634 That by placing certain bets, they could actually encourage the prize to roll over. It's it's described and so, once or twice a year, the expectation would go positive. 82 00:12:57.083 --> 00:13:06.683 And what the MIT students did is, they set up a send to get with a lot of people buying tickets all across the state and they would make deals I think, with. 83 00:13:07.649 --> 00:13:13.918 You know, convenience store owners to go in early or something, and just to buy tickets to the ticket printer burned out. 84 00:13:13.918 --> 00:13:21.208 And so, and it would go positive and they would, and they would make some money. Of course. 85 00:13:21.208 --> 00:13:27.899 You know, and they said, 201520% return and so you could there's a number of stories on this. 86 00:13:29.063 --> 00:13:40.524 So the thing is, this it was all totally legal, they were following the rules now since then the rules were changed, but it was all totally legal and they were buying a good fraction of all the tickets. 87 00:13:40.553 --> 00:13:52.524 I mean, I read 1 story that said for 1 lottery, MIT students, and their syndicate were buying 1, half of all the tickets sold in the whole state of Massachusetts. Now, of course, the state knew what was going on. 88 00:13:53.604 --> 00:14:07.344 But, you know, the lotteries profit for them, and so the more people buy tickets, they loved it, they were making money and of course, dollars per hour, it probably wasn't worth a lot, but it, what it worked. And now, by the way, there is a. 89 00:14:08.303 --> 00:14:19.104 So the state commissioned a report into what was going on and the report is quite detailed and it's public, and I'll put up the some time. So it's quite interesting reading. 90 00:14:19.104 --> 00:14:31.974 It's about what was done and then the state there were bad optics. These MIT students winning most of the prizes, so it was bad publicity. So the messages change the rules. 91 00:14:32.364 --> 00:14:44.933 The other thing is they, the MIT syndicate was not the only people doing this. There was another syndicate unrelated, which was also doing this, and they might have ended up on 60 minutes at some point. So. 92 00:14:45.389 --> 00:14:52.859 In any case, this is the stuff you learned in the course, could actually make you money. Um. 93 00:14:52.859 --> 00:14:59.158 Okay, so there's that of course, there's another way to. 94 00:15:00.839 --> 00:15:11.573 You know, there was another way that the security director of a multi state lottery was making money a couple years ago, and he made it by cheating. 95 00:15:11.964 --> 00:15:18.413 So he a couple times a year for certain balls to be drawn, or hacked the software or something. 96 00:15:18.989 --> 00:15:30.359 But he was caught because now you've got a winning chicken, how you cash it out. So he's now in prison I believe. So don't do that. Okay. So following sort of along what, Richard. 97 00:15:30.359 --> 00:15:33.418 Play Baccarat. Okay. Can you make it work? 98 00:15:33.418 --> 00:15:44.068 Mit, you know, maybe you could, but, you know, it's dollars for our counted cards. Yeah. That's the beat the dealer thing. Edward Thorpe I told you about. 99 00:15:44.068 --> 00:15:54.298 The, as you draw the car deck, if there's more tens or a fewer tens, an average that swings the odds, it doesn't swing them a lot towards you. But sometimes. 100 00:15:54.298 --> 00:16:06.899 And they also MIT students claim that they found a symmetry and reelect wheels once that wheels got old and worn. And that was you demonic high book that I, um. 101 00:16:07.254 --> 00:16:17.094 Had the reference to on Amazon last time. So well, of course, you know, it's only the real people try to play, um, Wall Street and so on. 102 00:16:18.443 --> 00:16:29.333 But if you're going to use your probability ideas to play Wall Street, there is an old joke about. How do you make a small fortune on Wall Street and anyone know how you make a small fortune on Wall Street. 103 00:16:32.339 --> 00:16:36.328 Start with the big 1. well, that too but, um. 104 00:16:46.678 --> 00:16:56.668 2nd here. Oh. 105 00:16:56.668 --> 00:17:00.418 Pump and dump. Okay start read it. 106 00:17:00.418 --> 00:17:03.479 Any stock or the guaranteed way. 107 00:17:05.009 --> 00:17:10.888 You got it Michael yeah. This joke goes back to that. I start with a large fortune. Yeah. 108 00:17:12.834 --> 00:17:27.413 There's another Wall Street joke that some group from the sticks already, let's say is going down in New York City, and he's being shown around all of any city. He's been in front of New York City, and somebody says in the harbor, look at all those yachts and the harbor. 109 00:17:27.864 --> 00:17:30.624 Those are the yachts of the brokers on Wall Street. 110 00:17:30.989 --> 00:17:35.909 So this country heck from Albany as well. That's nice where the customer is yachts. 111 00:17:35.909 --> 00:17:40.108 Okay, that can probability now. 112 00:17:40.108 --> 00:17:47.759 And not so easy to get the camera pointing at me because I got the camera on another machine. Okay. 113 00:17:47.759 --> 00:18:00.509 So, also, if I could, I'm 2nd, here, I'm, I'm gonna try something that may lock me up and I want to give it a try. Um. 114 00:18:01.919 --> 00:18:05.308 Alright, here. 115 00:18:20.368 --> 00:18:23.729 No, check in here. 116 00:18:25.739 --> 00:18:31.919 I'm trying to share the hover cam, which has which failed the last 5 times I tried, but I'm stubborn. 117 00:18:33.778 --> 00:18:43.648 So, we'll see if it shares here. Okay. 118 00:18:56.038 --> 00:18:56.788 Character 119 00:19:10.913 --> 00:19:11.574 wow. 120 00:19:11.848 --> 00:19:15.749 It actually worked I'm pleasantly surprised so. 121 00:19:18.148 --> 00:19:21.388 If we go back to. 122 00:19:22.558 --> 00:19:25.979 Axioms and probability and. 123 00:19:28.828 --> 00:19:33.628 I'd like to show, I'd just like to show you some, some other points from here. 124 00:19:33.628 --> 00:19:36.808 Let me use another example. 125 00:19:36.808 --> 00:19:44.189 And, I mean, I'm just going to take 1 die and try to motivate some of this. 126 00:19:44.189 --> 00:19:54.479 Okay, and. 127 00:19:54.479 --> 00:20:05.219 Simple discreet probability. I'm going to do it, you know, a fair. 128 00:20:07.499 --> 00:20:12.209 Excited guy, let's say, so our sample space. 129 00:20:16.288 --> 00:20:23.338 Okay, now we can have various some cells are outcomes. Now we could have various events actually. 130 00:20:23.338 --> 00:20:27.479 You know, let's see event a, is even. 131 00:20:29.429 --> 00:20:32.818 So, it's some 2 4. 132 00:20:32.818 --> 00:20:36.358 6 event B is say. 133 00:20:36.358 --> 00:20:41.338 A prime, so. 134 00:20:41.338 --> 00:20:44.818 2, 3 5. 135 00:20:44.818 --> 00:20:48.568 Um, events C is square. 136 00:20:51.538 --> 00:20:58.499 And 1 for okay, so now we can start and by the way. 137 00:20:58.499 --> 00:21:01.888 So this is anticipating a little, um. 138 00:21:01.888 --> 00:21:10.618 We need the abilities of the individual. 139 00:21:12.749 --> 00:21:20.368 Outcomes. Okay, so now, how you do that that that's another question and. 140 00:21:24.419 --> 00:21:31.769 And it's another question. Okay use physics you use whatever. 141 00:21:31.769 --> 00:21:36.328 Page 1, by the way. 142 00:21:38.038 --> 00:21:45.538 Physics commonsense, whatever. 143 00:21:45.538 --> 00:21:52.679 Okay, but this is a fair dye so that the probabilities are just a 2nd here. 144 00:21:52.679 --> 00:22:01.048 Okay. 145 00:22:03.628 --> 00:22:07.739 On, um, I'm just trying to get the chat window up. 146 00:22:13.169 --> 00:22:19.828 I was trying to get the chat window up so so I can see if people post questions. 147 00:22:19.828 --> 00:22:33.778 And, yeah, I'm not completely confident that if you, if you report a problem, I'll see it, but I'm hoping I will so it's. 148 00:22:33.778 --> 00:22:38.038 Complicated. 149 00:22:39.179 --> 00:22:45.239 Let's see ignore that. 150 00:22:50.969 --> 00:22:59.429 Well, okay, in any case. So, here so we assume is that. 151 00:22:59.429 --> 00:23:05.608 Say probabilities P, to say probability of 1 equals probability to. 152 00:23:05.608 --> 00:23:16.469 People say 1, 6. okay. You know, common sense physics. What? I'll get to that a little later in my blog. So now we can start talking about well, the probability of. 153 00:23:16.469 --> 00:23:24.179 A, which is even it's just going to be, you add the probabilities of the 3 separate outcomes and that's going to be 1 half. 154 00:23:24.179 --> 00:23:33.088 Sense okay, the the same thing, Prime, there's 3 separate outcomes that go into the prime event and so that will be. 155 00:23:33.088 --> 00:23:36.148 1, half also, um. 156 00:23:36.148 --> 00:23:39.689 And probability of see the 2 outcomes. 157 00:23:40.769 --> 00:23:49.138 Equals 4th now, you can start doing your combos and get get the combo things. Some of the formulas. 158 00:23:51.179 --> 00:23:56.669 By the way I, I'll. 159 00:23:56.669 --> 00:24:00.689 This, and I'll scan it in after. 160 00:24:00.689 --> 00:24:05.368 Okay, do something like that. 161 00:24:05.368 --> 00:24:09.179 Okay, so now we can start talking about. 162 00:24:09.179 --> 00:24:14.759 Say, the probability of a intersect be so both those things and. 163 00:24:14.759 --> 00:24:19.679 So, for something simple, like this, all you do is, you count you, you just look at it. 164 00:24:19.679 --> 00:24:22.769 And to a intersect B, so. 165 00:24:22.769 --> 00:24:28.979 A intersect me that's going to be even in prime, so that's 2. 166 00:24:28.979 --> 00:24:33.929 6, and then probably. 167 00:24:33.929 --> 00:24:38.759 So a union B is going to be the set of even. 168 00:24:38.759 --> 00:24:44.939 Or Prime, and that is going to be everything, but 1. 169 00:24:48.118 --> 00:24:52.229 The probability of a union B, it was 5 6. 170 00:24:52.229 --> 00:24:57.568 So, now you can start getting these combo rules, like the probability. 171 00:24:57.568 --> 00:25:02.128 Of a union B equals a probability of a. 172 00:25:02.128 --> 00:25:07.439 Plus the probability of the minus, the probability of a intersect fee. 173 00:25:07.439 --> 00:25:13.048 This is 1 half. This is 1 half. This is minus. 174 00:25:14.219 --> 00:25:17.818 1, 6, and that will be. 175 00:25:18.868 --> 00:25:25.318 I6, okay now we can start doing, um. 176 00:25:25.318 --> 00:25:30.088 3 ways also, let me just try and. 177 00:25:33.749 --> 00:25:38.818 Okay, so 3 ways now, we can say. 178 00:25:38.818 --> 00:25:43.259 A 3 way call most. 179 00:25:43.259 --> 00:25:48.088 So, the probability of a union, the union C. 180 00:25:48.088 --> 00:25:51.179 Is the probability of a. 181 00:25:51.179 --> 00:25:55.108 Us the probability of the US, the probability you see. 182 00:25:55.108 --> 00:25:59.759 Minus the probability of a. 183 00:25:59.759 --> 00:26:07.108 Intersect me minus the probability. Be intersect. See minus of probability. They intersect. See. 184 00:26:07.108 --> 00:26:12.778 Plus the probability, uh, a intersect B intersect C. 185 00:26:12.778 --> 00:26:16.348 Let me find another caller. I have 1. 186 00:26:16.348 --> 00:26:23.788 And start, okay probability of a is. 187 00:26:23.788 --> 00:26:26.909 1, 1. 188 00:26:26.909 --> 00:26:34.199 When half a intersect B was 1 6 now be intersect. C. 189 00:26:34.199 --> 00:26:37.259 If we go back up to here. 190 00:26:38.909 --> 00:26:43.348 B is prime is square B intersect C. 191 00:26:43.348 --> 00:26:47.699 Is the empty set so the intersect see is 0. 192 00:26:47.699 --> 00:26:55.199 Um, a intersect see, even and square that's going to be 4. that's going to be a 6. 193 00:26:55.199 --> 00:27:04.739 A intersect B intersect C is going to be 0T because the intersect. So, um. 194 00:27:04.739 --> 00:27:07.858 So, it's even plus plant prime plus Square. 195 00:27:07.858 --> 00:27:12.388 Um, not that's nothing. Okay. 196 00:27:12.388 --> 00:27:16.348 So, now we can start adding it up. 197 00:27:16.348 --> 00:27:20.128 So that is 1 half. 198 00:27:20.128 --> 00:27:25.588 Plus 1, half plus 1, half minus 1, 6 minus 0. 199 00:27:25.588 --> 00:27:28.858 Minus 1, 6, plus 0. 200 00:27:28.858 --> 00:27:32.999 So, what do we have here? 3 have. 201 00:27:32.999 --> 00:27:36.209 Minus J. we have more than 1. 202 00:27:36.209 --> 00:27:42.209 Okay. 203 00:27:42.209 --> 00:27:46.259 Okay. 204 00:27:47.519 --> 00:27:50.548 I did I do wrong here. 205 00:27:55.318 --> 00:27:59.189 A chance for you to think about what I did wrong. 206 00:27:59.189 --> 00:28:03.239 Someone in the chat, the probability should be 4th proceed. 207 00:28:03.239 --> 00:28:08.068 Okay, I don't see. 208 00:28:08.068 --> 00:28:11.429 See square 4th, thank you. 209 00:28:11.429 --> 00:28:20.788 Very good. So, a half a half that's. 210 00:28:20.788 --> 00:28:24.659 Plus the 3rd, so this equals equals 1. 211 00:28:24.659 --> 00:28:29.429 So a intersect so a union B union C. 212 00:28:29.429 --> 00:28:34.739 A, is 2, 4, 6, 5 then we get a. 213 00:28:34.739 --> 00:28:40.138 Well, if we just count out, we've got 1 in here, 2 in here, 3 and here 4 in here. 214 00:28:40.138 --> 00:28:44.459 I've been here 6 in here, so that is. 215 00:28:47.068 --> 00:28:51.358 Okay, you see so we can do the 3 way thing. 216 00:28:52.949 --> 00:28:57.898 Shouldn't that Mohammed gets the point? Okay, Muhammad, send me email. 217 00:28:57.898 --> 00:29:00.898 Give me here, remind me. 218 00:29:00.898 --> 00:29:06.479 Shouldn't that changes the intersect? I don't understand your last point. 219 00:29:06.479 --> 00:29:09.568 So, you can turn your Mike on and tell me what you mean. 220 00:29:11.219 --> 00:29:15.298 Just a little here's how you got the. 221 00:29:15.298 --> 00:29:18.479 The a B, and the. 222 00:29:18.479 --> 00:29:25.199 The 4th and the 5th part of the, the, and I understand. Okay. Yeah. How you got the close. 223 00:29:27.538 --> 00:29:36.028 Well, this is simple enough. So, the question is a intersect. C well, the question is simple enough that I can just write it down. 224 00:29:36.028 --> 00:29:45.179 So, a, is, if I go back, I'm going to give you headaches if I keep flipping pages. So I'll just rewrite it. So a, is even so that's 2. 225 00:29:45.179 --> 00:29:49.588 4 6 C is square. 226 00:29:52.259 --> 00:30:01.078 So this is 1 for a intersect C it's doesn't have 1. it doesn't have to. It has just for. 227 00:30:01.078 --> 00:30:06.778 Okay, it's the only number that's an even square from 1 to 6. 228 00:30:08.368 --> 00:30:13.199 That makes sense. Yep. Got it. Thank you. Sure. Thanks. 229 00:30:13.199 --> 00:30:18.298 I didn't under your garbled, so it would be 1 of things. That's. 230 00:30:18.298 --> 00:30:23.009 And a price, so probability of a intersect. 231 00:30:23.009 --> 00:30:26.219 Is 1 over a 6 Thank you. Right? 232 00:30:26.219 --> 00:30:31.528 It's still a question about the triple thing if we have. 233 00:30:31.528 --> 00:30:39.269 A interesting. Okay. Good. I just put in the concept of intercept, but I do thank you. 234 00:30:39.269 --> 00:30:42.449 Good so you can, um. 235 00:30:45.838 --> 00:30:57.989 Right. So we have some examples here and here, here's the biggie right here for all 6, and just take it up. So as many as you just alternating um. 236 00:30:57.989 --> 00:31:06.778 Plus and minus, so there are some assumptions. So you assume. 237 00:31:08.308 --> 00:31:18.239 Independence and so so what that means is. 238 00:31:20.699 --> 00:31:27.778 Well, we're just having 1 paused right now, but no funny correlations and combos and things. Okay. 239 00:31:27.778 --> 00:31:34.169 Crawlers 7 here. Try yeah. 240 00:31:34.763 --> 00:31:45.534 Let me pull up, um, well, if 1 event has fewer outcomes is going to is contained in another event, then it's probably going to be smaller. 241 00:31:45.564 --> 00:31:50.453 So, if I've got here even in Square, and then. 242 00:31:50.729 --> 00:31:56.878 I mean, I could define say event the. 243 00:31:56.878 --> 00:32:03.148 Which is just outcome um, I don't know, just for something for some reason. 244 00:32:03.148 --> 00:32:06.929 Then the set, it's inside the set sea. 245 00:32:06.929 --> 00:32:11.729 So, the probability of the less faithful to the probability of C. 246 00:32:11.729 --> 00:32:18.239 And the probability of D here is going to be 1, 6 and probability of c4th. So. 247 00:32:19.409 --> 00:32:24.449 So. 248 00:32:24.449 --> 00:32:28.048 Probably D, it was 1 6. I'll receive. 249 00:32:28.048 --> 00:32:35.548 It was 1 search. Oh, okay. Okay. So this is great. Okay. Now. 250 00:32:35.548 --> 00:32:38.788 The next thing here, this is. 251 00:32:38.788 --> 00:32:42.689 So, how do we get the probabilities. 252 00:32:48.209 --> 00:32:51.628 For. 253 00:32:53.278 --> 00:32:57.689 Um, so. 254 00:33:01.019 --> 00:33:05.999 How to get you might say the low level probabilities. 255 00:33:10.409 --> 00:33:13.528 Let me give you an example, let's suppose the experiment. 256 00:33:15.929 --> 00:33:19.769 Is coin wise. 257 00:33:20.788 --> 00:33:25.169 Okay, um, and now. 258 00:33:25.169 --> 00:33:28.348 You know, you get. 259 00:33:28.348 --> 00:33:33.209 To define the outcomes. 260 00:33:35.909 --> 00:33:39.689 And Here's 1 idea, let's suppose the outcome. 261 00:33:39.689 --> 00:33:48.388 Is, um, is the number of heads. 262 00:33:48.388 --> 00:33:54.449 Okay, so the sample space is 0, 1 or 2. 263 00:33:56.189 --> 00:34:02.398 Um, what are the probabilities? Okay. 264 00:34:05.729 --> 00:34:10.378 Now, this is, this is a hard problem. This, this is genuinely hard. Um. 265 00:34:10.378 --> 00:34:13.949 Or you might say that the. 266 00:34:15.268 --> 00:34:24.539 This is hard, so we might say something like well, the problem is zeros. A probability of a 1 is a problem of a 2. 267 00:34:24.539 --> 00:34:27.778 It was 4th. 268 00:34:29.579 --> 00:34:42.028 Maybe there's some funny coins and but do you have any comments on that? We're tossing a coin twice or outcomes a number of heads? We see. It could be 0T heads 1 head or 2 had. 269 00:34:42.028 --> 00:34:47.969 And we might just say probability to these 3 possible outcomes or it's a 3rd. 270 00:34:49.469 --> 00:35:01.079 Comments on that. Is that even possible? Is it likely. 271 00:35:02.219 --> 00:35:11.338 Um. 272 00:35:11.338 --> 00:35:20.188 No, it's possible, but it's not likely and it's impossible if the coin tosses are independent of each other. 273 00:35:20.188 --> 00:35:26.579 Oh, by the way I've got to give another. 274 00:35:26.579 --> 00:35:33.119 Gambling job, you're in a poker game, and you look around the table and you can't tell who the mark is. 275 00:35:33.119 --> 00:35:37.889 Here are the mark. Okay. Um. 276 00:35:42.478 --> 00:35:50.338 And it's not possible if the. 277 00:35:50.338 --> 00:35:56.278 Utah says independent. 278 00:36:01.259 --> 00:36:12.028 Okay, oh, by the way, if you're wondering why I'm using a low tech pen and pad of paper and hover cam instead of events, the. 279 00:36:12.028 --> 00:36:15.208 Not taking application on my computer. 280 00:36:15.208 --> 00:36:19.139 Is that if I can get it working the pen and paper is faster. 281 00:36:20.309 --> 00:36:28.318 So, professor, yes question, because Andrew personally, in chat that I think I agree with. 282 00:36:28.318 --> 00:36:34.139 When he talks about the problem is the 2000 part of the coin tosses. 283 00:36:34.139 --> 00:36:39.898 Your best your sample space, you're saying you either get 0T heads 1 head or 2. 284 00:36:39.898 --> 00:36:46.798 But aren't the possible outcomes like, wouldn't the probability not be 100? Because you could either get. 285 00:36:46.798 --> 00:36:50.248 Do you have you're more probable to get. 286 00:36:50.248 --> 00:36:54.958 1 head, because of the 2 tosses, you kind of get head tails or hotel heads. 287 00:36:54.958 --> 00:37:09.898 Right, exactly Thank you. Um, well, that's the independent thing there that if the 2 tosses, if you tossed once and head sales thoughts again, and heads tails and you're going to get what you say, the probability of exactly. 1 head. 288 00:37:09.898 --> 00:37:14.099 It is on 1 half yeah. 289 00:37:14.099 --> 00:37:28.048 The only way you're gonna get equal a 3rd, a 3rd, a 3rd, is that some crazy experiment where the 2 tosses are tied to each other somehow? And it's, you're in Las Vegas pulling, you know. 290 00:37:28.048 --> 00:37:42.958 A slot machine and everything is computer generated, you could generate whatever you want, but right. But this is the thing I'm saying about, it's hard. It's hard to figure this out, but you're right assuming the common sense case that tossed the coin. 291 00:37:42.958 --> 00:37:50.489 Heads or tails, he talks the coin again heads or tails then you're going to get what you said and you're going to get. 292 00:37:52.469 --> 00:37:57.509 And going to see if I can do something like this up here. 293 00:37:57.509 --> 00:38:01.289 Okay. 294 00:38:02.458 --> 00:38:06.418 So, the, the reasonable. 295 00:38:10.858 --> 00:38:14.639 Is, um, right. 296 00:38:14.639 --> 00:38:19.260 Probability is 0T heads is 1 quarter? Probably do 1 had. 297 00:38:19.260 --> 00:38:24.539 Is 1 half the probably 2 heads is 1 quarter because. 298 00:38:27.420 --> 00:38:32.639 Um, you know, if you look at it another way. 299 00:38:35.699 --> 00:38:44.639 If you're looking at this sort of detailed outcomes of, um, you know. 300 00:38:44.639 --> 00:38:47.730 And then s would be say kale kale. 301 00:38:47.730 --> 00:38:51.750 Gale head and tail and had. 302 00:38:51.750 --> 00:38:59.489 And for each toss, then you're going to get. 303 00:38:59.489 --> 00:39:03.210 At tail and it's 1 half 1 half. 304 00:39:03.210 --> 00:39:09.000 So these things here is going to be a quarter quarter 1 quarter 1 quarter. Yeah. 305 00:39:09.000 --> 00:39:15.929 Yeah, now the reason I'm spending a little time on this. 306 00:39:15.929 --> 00:39:27.030 Is this 2 coin costs thing? It's obvious, but we can get a little fancier and it's not obvious actually. And people can can start arguing about it. Um. 307 00:39:27.030 --> 00:39:33.539 So, I mean. 308 00:39:34.559 --> 00:39:37.590 This 1 is easy. 309 00:39:38.639 --> 00:39:44.579 Here's an example harder was something called a Monty all problem. 310 00:39:47.639 --> 00:40:01.559 Um, cause arguments see, if I can find so getting these probabilities let's see. 311 00:40:13.920 --> 00:40:21.900 So, you may have seen it yeah. 312 00:40:21.900 --> 00:40:29.460 The game show choice of 3 doors behind 1 doors, a car to others coats assumption. You like a car more than a call. 313 00:40:29.460 --> 00:40:36.750 You never know, and you pick a door and the host knows it behind the door. 314 00:40:36.750 --> 00:40:42.239 Opens another door, which has a goats and he says, do you want to switch or not? And. 315 00:40:42.239 --> 00:40:50.909 This is the sort of thing people argue about the probabilities and so on. So that's why like I said, I do the switch. Okay. This. 316 00:40:50.909 --> 00:40:54.719 Always, yeah, so you can work that 1 out. 317 00:40:54.719 --> 00:40:59.400 Oh, okay. Any case back to the stuff I typed in here. 318 00:40:59.400 --> 00:41:02.639 Um, just create sample space. 319 00:41:04.139 --> 00:41:15.659 On probabilities. Okay. H, here, I did what I wrote down on the blog on the paper, but H, here is just with 3 coins and just to make it a little harder. 320 00:41:15.659 --> 00:41:20.460 So again, so the experiment is pasta coin. 3 times. 321 00:41:20.460 --> 00:41:29.789 Again, you're, you're in the experimenter, you can say what the outcomes are what you're looking at. I mean, it could be an outcome is where the coin lines on the floor. 322 00:41:29.789 --> 00:41:34.800 You know, if that's what you're interested in, or it could be, um. 323 00:41:34.800 --> 00:41:38.159 The number of had heads, or it could be. 324 00:41:38.159 --> 00:41:43.230 You know, the detailed thing, the 3 coin sequence, tail, tail head or something. 325 00:41:43.230 --> 00:41:47.969 And the point here is that it's, um. 326 00:41:47.969 --> 00:41:53.579 You may have to add assumptions or do experiments or something so. 327 00:41:53.579 --> 00:41:56.969 Okay, so. 328 00:41:56.969 --> 00:42:11.429 That was more detailed, discreet case. The countably infinite case number of tosses. You get the 1st head half the time happens on the 1st, toss part at the time that happens on the 2nd costs and so on. And the sum to 1. 329 00:42:11.429 --> 00:42:14.670 Okay, and. 330 00:42:16.050 --> 00:42:21.480 Formula, I don't know, I take in high school if it's a good high school, but how these things. 331 00:42:21.480 --> 00:42:28.349 So, um, and. 332 00:42:28.349 --> 00:42:37.230 So you might say, what is the sum of 1 half. 333 00:42:37.230 --> 00:42:40.590 Plus 1 quarter, plus 1 age. 334 00:42:40.590 --> 00:42:46.469 You know, 1, over 2 to the, um, K. 335 00:42:48.539 --> 00:42:53.130 And so on, and there's different ways you can solve it. Um. 336 00:42:54.420 --> 00:43:02.730 And we could let that be a, Here's 1 way you could solve it. Let's say, um. 337 00:43:05.369 --> 00:43:17.670 1, half plus 1 quarter, this equals 1 half plus a sum of 1 quarter plus 1 H busted and this thing here. 338 00:43:21.659 --> 00:43:34.800 i just take a half out of here and this is up to infinity so what we've got is a equals on half plus one half a and um . 339 00:43:36.659 --> 00:43:41.909 So this implies a equals 1, 1 way to solve it. So. 340 00:43:41.909 --> 00:43:49.349 Okay, okay so countably in finance um. 341 00:43:50.489 --> 00:43:54.690 The continuous case we had that last time um. 342 00:43:54.690 --> 00:43:59.400 And you have to work with intervals so the probability. 343 00:43:59.400 --> 00:44:02.400 You can add show. 344 00:44:04.199 --> 00:44:17.909 Can do something like again just remind you I did this last time. Well, uniform. 345 00:44:21.840 --> 00:44:25.139 I'm supposed to uniform from 0T to 1. 346 00:44:25.139 --> 00:44:28.530 So, probably he said X is from a, to B. 347 00:44:28.530 --> 00:44:41.130 It was 1 minus FEMA and say we saw that last time. Okay if you want mathematical rotation called this sort of thing of where else that we work with probabilities on intervals. Okay. 348 00:44:42.389 --> 00:44:47.130 Non uniform distributions are common I showed you the radioactive decay. 349 00:44:47.130 --> 00:44:51.119 Now, you could get a combo. 350 00:44:54.420 --> 00:44:57.809 Do you mind here of a combo distribution? 351 00:44:57.809 --> 00:45:07.860 Up here. 352 00:45:16.619 --> 00:45:19.920 A combo type, so. 353 00:45:21.960 --> 00:45:26.579 You're you're waiting for a car. 354 00:45:26.579 --> 00:45:31.889 At the airport. Okay. 355 00:45:34.289 --> 00:45:38.730 And he is the time waiting. 356 00:45:40.800 --> 00:45:43.860 So maybe the cards there when you get there. Okay. 357 00:45:43.860 --> 00:45:53.730 Probably you don't wait at all is 1 half. Okay. The car's there but if the car is not there, you're going to wait an exponential time or something. 358 00:45:53.730 --> 00:45:59.250 So, the probability of waiting key with tea, greater than 0. 359 00:45:59.250 --> 00:46:03.750 Um, oh, okay. 360 00:46:03.750 --> 00:46:07.320 The probability of waiting. 361 00:46:07.320 --> 00:46:12.239 Some time greater than some parameter. 362 00:46:14.460 --> 00:46:17.789 Is this big piece of some sort of parameter? 363 00:46:17.789 --> 00:46:20.820 And little cheesier, random variable. 364 00:46:24.539 --> 00:46:28.409 So the probability you're waiting a time greater than tea. 365 00:46:28.409 --> 00:46:33.239 Might be something like, I don't know, um. 366 00:46:38.369 --> 00:46:42.780 See is just a constant I put in there, so we'll integrate out to 1. 367 00:46:44.849 --> 00:46:47.880 So, it's a combo, so. 368 00:46:47.880 --> 00:47:02.094 These precise time as 0T has their profitability is 50, 50, but then if not, then it's a continuous distribution. And all we can talk about is the time that there's an interval. And this is a reasonable example here. Okay. 369 00:47:02.485 --> 00:47:06.655 I don't know what C is to have to work it out. It's 1 half perhaps but. 370 00:47:06.960 --> 00:47:11.309 And this would be an exponential distributor and this is actually. 371 00:47:11.309 --> 00:47:16.349 Sort of reasonable here. Oh, okay. 372 00:47:16.349 --> 00:47:21.329 Like, so. 373 00:47:21.329 --> 00:47:25.889 You get this thing, you might have specific points and so on. 374 00:47:28.769 --> 00:47:32.369 And just throwing another light thing here. 375 00:47:40.139 --> 00:47:46.050 Okay, the claim of this article is that you can toss a coin. So as. 376 00:47:49.320 --> 00:47:53.699 Okay, on football, the, um. 377 00:47:53.699 --> 00:47:57.539 The way they do it is, you know, 1 is the other calls so. 378 00:47:57.539 --> 00:48:02.429 Okay, did you do. 379 00:48:03.510 --> 00:48:07.769 So Here's a real example of non uniform. 380 00:48:07.769 --> 00:48:15.030 The continuous probability thing. Okay. Um, there's exponential distribution again. Does this? Okay so. 381 00:48:37.769 --> 00:48:42.570 So, does, is this a legal probability distribution? Well. 382 00:48:42.570 --> 00:48:46.559 Individual probabilities are non negative um. 383 00:48:46.559 --> 00:48:52.380 The probability of some of anything at all happening is 1, that would be TV. 0. 384 00:48:52.380 --> 00:49:01.050 And, yeah, so this is legal and for a final interval, you to find something like this, this here is a legal. 385 00:49:01.050 --> 00:49:05.099 Legal interval legal probability definition. Okay. 386 00:49:06.329 --> 00:49:13.500 So, and again, this would be the sort of thing, chip lifetime, perhaps radioactive decay. 387 00:49:13.500 --> 00:49:17.130 Stuff like this, so it's things like this happen sometimes. 388 00:49:17.130 --> 00:49:30.929 And again, not chip lifetime if you're going to use this, you got to have some reason for thinking that this is reasonable for the chip. And I'm guessing I'm a software type. This is actually probably not a good, probably distribution for a chip, but. 389 00:49:30.929 --> 00:49:40.469 Another example of a continuous thing, and this will give us a chance to throw in some of these combo things. Um. 390 00:49:42.329 --> 00:49:47.789 See here share my screen. 391 00:49:50.760 --> 00:49:55.079 Okay. 392 00:49:56.309 --> 00:49:59.369 So, we are, um. 393 00:50:00.630 --> 00:50:05.909 You go to square here it's 1 by 1. 394 00:50:05.909 --> 00:50:10.650 And we are picking points randomly in the square. 395 00:50:10.650 --> 00:50:17.369 And again, it's non countably infinite the probability of any specific point. 396 00:50:17.369 --> 00:50:23.340 Is 0T however, but we can talk about combo things like. 397 00:50:23.340 --> 00:50:27.840 Like, here, we might get this, this might be event a here. 398 00:50:27.840 --> 00:50:31.199 So, a is the event this is X. 399 00:50:31.199 --> 00:50:34.230 This is a, is the event that Y. 400 00:50:34.230 --> 00:50:38.909 Cinco to 1. half. Okay. How good is a. 401 00:50:38.909 --> 00:50:43.199 Equals 1 half, we might get a 2nd thing. Um. 402 00:50:43.199 --> 00:50:47.909 The whole screen on here. Okay. Um. 403 00:50:52.739 --> 00:50:57.750 This is B, he is the probability that, um. 404 00:50:57.750 --> 00:51:08.309 That X is greater than why probability would be to be there. There's also 1 half. Okay. Now I can start getting. 405 00:51:08.309 --> 00:51:12.869 Things like, I might say C is a intersect be. 406 00:51:12.869 --> 00:51:16.679 Okay, so that is going to be, um. 407 00:51:20.639 --> 00:51:25.679 Okay, and that is going to be a. 408 00:51:28.230 --> 00:51:31.260 The 2, 3, 8, so I think. 409 00:51:36.900 --> 00:51:40.889 Okay, and we could get, um. 410 00:51:40.889 --> 00:51:45.449 He is, is a union be. 411 00:51:45.449 --> 00:51:53.519 And that is probably is 5, 8. 412 00:51:53.519 --> 00:51:57.690 And now we can start saying things like. 413 00:51:57.690 --> 00:52:02.369 So a union B is a. 414 00:52:02.369 --> 00:52:08.190 Us B, that's 1 minus 3 H, which gives 5 dates and so on. So we can apply. 415 00:52:08.190 --> 00:52:12.929 This now this is assuming this uniform. 416 00:52:12.929 --> 00:52:16.380 Um, distribution, so. 417 00:52:20.340 --> 00:52:33.809 And this is important. Yeah. Is it true? 418 00:52:36.809 --> 00:52:45.780 Um, you know, well, if it's in this course, and I gave you a homework, things are going to tell you it. So it's true because I told you so, and I never make mistakes as, you know, okay. 419 00:52:45.780 --> 00:52:50.639 Want to give it out to no at all points so far. Okay in the real world. 420 00:52:50.639 --> 00:52:54.780 You know, you got to have some reason for assuming it's true. 421 00:52:54.780 --> 00:52:58.980 And give you a case, maybe false. Um. 422 00:53:11.699 --> 00:53:15.869 You're trying to hit a target. Okay. 423 00:53:17.429 --> 00:53:23.369 Um, okay. 424 00:53:23.369 --> 00:53:29.639 So the point to not uniform. 425 00:53:30.929 --> 00:53:35.010 Well, I don't know how good you are hitting the target. You you see the point I'm making. 426 00:53:35.010 --> 00:53:40.920 Okay, I keep coming back to that, because in the real world, um. 427 00:53:40.920 --> 00:53:44.820 I'm assuming you guys are smart. Okay you're going to get the math um. 428 00:53:44.820 --> 00:53:53.039 And so once you understand the math, the next question is what's the correct math to use. 429 00:53:53.039 --> 00:54:05.340 And so, and we get economics problems in the real world, caused by very smart people using the wrong math. So they can cause major economic crashes and so on. So. 430 00:54:05.340 --> 00:54:08.460 I put a link in to a question or 2 at some point. 431 00:54:08.460 --> 00:54:12.719 Um, my again. 432 00:54:12.719 --> 00:54:16.739 So so some recap here. 433 00:54:16.739 --> 00:54:20.340 We got random experiments. 434 00:54:22.409 --> 00:54:27.989 And, okay, so every time you do the experiment, you. 435 00:54:27.989 --> 00:54:34.860 Get a different answer, but you define the experimental procedure and you define the set of. 436 00:54:34.860 --> 00:54:46.590 Measurements um, yes, sorry, I'll mute. Okay. Sample space and so on. 437 00:54:46.590 --> 00:54:50.340 Okay, um, and I'd like. 438 00:54:50.340 --> 00:54:53.340 To I want to mention it. 439 00:54:53.340 --> 00:55:00.570 In, um, and stuff like that, just a quick introduction to that. And then. 440 00:55:04.170 --> 00:55:09.090 Um, I'll put up a bot because I'm listing some of this as. 441 00:55:09.090 --> 00:55:19.440 It's Rad, key stuff to watch and so so sort of question is this. 442 00:55:21.900 --> 00:55:31.920 Let's say, pass the coin end times. 443 00:55:35.010 --> 00:55:39.059 Lots of probability of K heads. 444 00:55:41.130 --> 00:55:46.829 Okay, um, so we found the probability of, um. 445 00:55:46.829 --> 00:55:59.789 So, we found, for example, if N, equals to toss it twice, then we got the probabilities for 1 quarter 1, half 1 quarter for k0 1 and 2 and so on. 446 00:55:59.789 --> 00:56:03.119 Anticipating. 447 00:56:03.119 --> 00:56:10.050 So, we want to generalize this. Okay. And. 448 00:56:13.230 --> 00:56:19.469 With an equal 3, then the probabilities are 9th. 449 00:56:19.469 --> 00:56:22.590 3, 3, 8 wanting. 450 00:56:22.590 --> 00:56:25.590 And how do we get that? 451 00:56:25.590 --> 00:56:33.659 Well. 452 00:56:35.880 --> 00:56:43.019 So the probability I'll just say of 1 head. 453 00:56:44.789 --> 00:56:49.829 And 3 tosses, it's a number of ways. 454 00:56:52.980 --> 00:56:56.519 You can get 1 head. 455 00:56:57.630 --> 00:57:04.500 2 tails divided by 8, the number of different combos. So it'd be head tail tail. 456 00:57:04.500 --> 00:57:08.880 Ever had kale kale, tail head. 457 00:57:08.880 --> 00:57:15.090 3 of them, so the probability is 3 over 8 because this 8 here. 458 00:57:15.090 --> 00:57:18.780 That's the total number of ways. 459 00:57:20.699 --> 00:57:25.530 Okay, and you can generally and there's a formula for it. 460 00:57:25.530 --> 00:57:29.190 Um, and so generally. 461 00:57:29.190 --> 00:57:33.690 For a heads. 462 00:57:35.400 --> 00:57:38.820 Probability is some, this is a notation it's called. 463 00:57:38.820 --> 00:57:46.170 And choose K and it's equal to N factorial. 464 00:57:46.170 --> 00:57:50.369 Over K factorial and minus K factorial. 465 00:57:50.369 --> 00:57:53.670 How many people have seen something like this. 466 00:57:53.670 --> 00:57:58.590 That calibrate me. No. Okay. 467 00:57:58.590 --> 00:58:03.329 Once Yep, anyone in Fox has a. 468 00:58:04.440 --> 00:58:07.590 Reason for making Fox a prerequisite. 469 00:58:07.590 --> 00:58:16.110 Okay, but not everyone is necessarily remembers that any I'll go through this quickly then. So this is a number of ways. 470 00:58:16.110 --> 00:58:19.260 This is the probability getting exactly. K heads. 471 00:58:19.260 --> 00:58:22.349 Um, and so. 472 00:58:22.349 --> 00:58:25.530 So, for example. 473 00:58:25.530 --> 00:58:34.199 Here problem is, is I can't zoom the hover cam and it doesn't quite. 474 00:58:34.199 --> 00:58:38.400 Show the whole range. Okay. 475 00:58:38.400 --> 00:58:41.730 So, for example. 476 00:58:41.730 --> 00:58:49.469 Oh, okay. So, for example, um, say can choose 5. 477 00:58:49.469 --> 00:58:53.579 That's going to be 10 factorial over. 478 00:58:57.570 --> 00:59:02.639 Fact for, and that's approximately 1 quarter actually. Okay. 479 00:59:03.385 --> 00:59:15.744 Now, going ahead. A little if N. K. A. very large. There are good approximations for this. There's something called a normal distribution to the law of large numbers and so on. So, this is a quick introduction to. 480 00:59:18.329 --> 00:59:25.889 You want to count the number of you count the number of combinations of. 481 00:59:25.889 --> 00:59:29.099 Say, 5 heads and 5 tails. 482 00:59:30.210 --> 00:59:36.630 So, and here, the tosses are unrelated to each other. 483 00:59:36.630 --> 00:59:39.719 Let me give you a slightly different model. 484 00:59:39.719 --> 00:59:46.650 Um. 485 00:59:48.389 --> 00:59:56.309 Age 10 motivate a different model here for you do. 486 00:59:57.329 --> 01:00:00.389 Earn Where's my. 487 01:00:02.610 --> 01:00:05.760 Silence. 488 01:00:07.469 --> 01:00:16.530 So, once upon a time people paid with things called. 489 01:00:16.530 --> 01:00:20.699 Point okay. And. 490 01:00:20.699 --> 01:00:25.139 The idea is that you draw a. 491 01:00:25.139 --> 01:00:29.610 I don't know how many coins I've got here. 2. 3. 492 01:00:29.610 --> 01:00:35.369 45678 91011. 493 01:00:35.369 --> 01:00:40.079 I haven't coins here and I, I might want to talk about. 494 01:00:40.079 --> 01:00:43.500 Number of ways I can draw. 495 01:00:43.500 --> 01:00:49.949 And I'm drawing coins at random. I just pick 1 coin out of the 11 coins at random equal. 496 01:00:49.949 --> 01:00:55.320 Each coins and equal probability and then I'd want to find. 497 01:00:55.320 --> 01:00:59.309 Well, if I pick 1 coin out. 498 01:00:59.309 --> 01:01:03.449 And say, you know, the number of ways, I can pick a quarter. 499 01:01:03.449 --> 01:01:07.530 Okay, that's a quarter. Well. 500 01:01:07.530 --> 01:01:12.329 I could I could pick a quarter this way. I could pick a quarter that way. 501 01:01:12.329 --> 01:01:16.800 There's how many quarters do we have in here? 502 01:01:16.800 --> 01:01:23.969 5 quarters, so the number of ways I could pick a quarter there are 5 out of the 11 waste and so on. 503 01:01:27.719 --> 01:01:38.519 But we can start talking about now probabilities are probably the picking up quarters 511st. We might talk about the number of ways. We could pick a. 504 01:01:38.519 --> 01:01:43.739 Border and a, a dime, let's say. 505 01:01:43.739 --> 01:01:49.380 Now, given I've got 5 borders and, um. 506 01:01:49.380 --> 01:01:53.280 2 times. 507 01:01:53.280 --> 01:01:59.340 So so let me. 508 01:01:59.340 --> 01:02:06.030 11 coins. 509 01:02:06.030 --> 01:02:10.829 5 quarters the dimes. 510 01:02:11.849 --> 01:02:18.269 Um, let's see. 511 01:02:20.909 --> 01:02:25.949 To Nicole. 512 01:02:27.659 --> 01:02:32.460 2 pennies, it adds up to 11. what do you know. 513 01:02:32.460 --> 01:02:36.119 Um. 514 01:02:39.929 --> 01:02:43.590 So, now, the saying is get a little tricky because. 515 01:02:43.590 --> 01:02:48.599 And we could call this little thing here in earn. Okay. 516 01:02:52.619 --> 01:02:56.880 And just a little container, let's say okay, so. 517 01:02:59.760 --> 01:03:05.639 So, you got the probability of draw a quarter draw, just be full of quarter out. 518 01:03:06.780 --> 01:03:12.989 It goes 5 elevens veiled here. The dime. 519 01:03:14.250 --> 01:03:17.909 Let's do 11. 520 01:03:21.119 --> 01:03:28.590 2 quarters. Okay. Now this gets no. Okay so the 1st quarter. 521 01:03:28.590 --> 01:03:31.800 Is so this is going to be the probability. 522 01:03:31.800 --> 01:03:38.730 Of a quarter and then. 523 01:03:38.730 --> 01:03:49.230 Draw another. I'm assuming I can all apply them. I'm going to waive my hands and and so on. 524 01:03:49.230 --> 01:03:55.619 Hope you don't ask questions. Okay. 1st, quarter. I said it is 511. 525 01:03:57.300 --> 01:04:02.969 But now, here, it gets tricky probably drawing the next quarter. It's not 5 elevens because. 526 01:04:02.969 --> 01:04:08.369 When we're here at the start, we had 11 coins. There's 5 quarters. 527 01:04:08.369 --> 01:04:15.119 Here we have 10 coins and there's 4 quarters. So this is 4 chance. 528 01:04:15.119 --> 01:04:21.599 Um, for the 2nd draw. 529 01:04:24.090 --> 01:04:28.980 You in the 1st coin was a quarter. 530 01:04:32.369 --> 01:04:37.440 We have now and coins. 531 01:04:37.440 --> 01:04:49.679 4 quarters you see, it's not it's not 5 out of 11. it's 4 out of 10. so this is called drawing without replacement. 532 01:04:58.980 --> 01:05:03.090 We might say drawing with replacement. 533 01:05:03.090 --> 01:05:06.539 By 11 times 410. 534 01:05:06.539 --> 01:05:10.260 Okay, so is. 535 01:05:10.260 --> 01:05:15.239 Yeah, do all right you see so. 536 01:05:16.860 --> 01:05:30.804 Without replacement and probability shift as you do this, like, playing Black Jack or something as they draw cards from the deck, then without drawing them without replacement. So on. So, this is an introduction to. 537 01:05:32.190 --> 01:05:36.960 So, you talk about the probability of drawing certain combinations. 538 01:05:36.960 --> 01:05:48.989 Of things here and so video will talk about that. I'll put some notes up on probabilities of that sort of thing. 539 01:05:48.989 --> 01:05:54.480 And introduce you some of the weird things that can happen. 540 01:05:55.559 --> 01:06:00.869 That could be a nice point to stop. Actually I'll scan these things in and put them up. 541 01:06:00.869 --> 01:06:06.329 And come back up here to the so what we're looking at. 542 01:06:06.329 --> 01:06:11.550 Is that the, like, fun stuff? Your profit and the real world. 543 01:06:11.550 --> 01:06:15.090 These ways you to combo things here. 544 01:06:15.090 --> 01:06:28.409 And I gave you examples, discrete sample space. The reason I'm pounding home these simple little things is that you got to get the foundations done, right? Otherwise. 545 01:06:28.409 --> 01:06:31.619 Eventually you get hassled. 546 01:06:31.619 --> 01:06:39.750 The probabilities of the outcomes you got to use something outside this course, physics or common sense or something. 547 01:06:39.750 --> 01:06:47.820 The outcomes are not always equal, but the point 1 yeah, this is a policy. If you see probability use in the real world people talk about. 548 01:06:47.820 --> 01:06:57.985 Probability of life on other planets or whatever, and they say, oh, these 20 separate things have to occur and we don't know if they're true or false. 549 01:06:57.985 --> 01:07:08.574 So, we're just going to say it was 50, 50 each time and we're going to assume these 20 separate things are all independent of each other. So, the probability of the 20 things all being too simultaneously is. 550 01:07:09.539 --> 01:07:16.050 1, in a 1M, this is total BS because just because you don't know anything about it doesn't mean the probability is 50%. 551 01:07:16.050 --> 01:07:26.250 And you have to have some reason for assuming they're independent. So, this thing about, and the thing here, if you're making your outcome from 3 tosses to be the number of heads. 552 01:07:26.250 --> 01:07:34.920 So, there's 4 possible outcomes you cannot just assume, therefore, are equal. So, and in fact, in this case, they're not the coins are independent. So. 553 01:07:34.920 --> 01:07:38.969 And it's all in this little case, but, you know, you can get. 554 01:07:38.969 --> 01:07:43.409 Situations that are complicated enough that it's not obvious where they're screwed up. 555 01:07:43.409 --> 01:07:47.369 So, countably infinite. 556 01:07:47.369 --> 01:07:51.389 Typical 1, number of costs to you succeed. 557 01:07:51.389 --> 01:08:00.750 There's a gambling policy where every time you lose you double the bed and re bathroom and eventually you're going to win when you win, you'll make money. It's the St Petersburg paradox. 558 01:08:00.750 --> 01:08:09.840 It has problems because eventually that's going to be so big that that here over the house limit continuous space as intervals. 559 01:08:09.840 --> 01:08:16.560 Real number, you can get a combo, continuous and discreet case. Like you're waiting for a car at the airport. 560 01:08:16.560 --> 01:08:23.640 I'm heading to pick up my wife at the airport after this class she's flying in from Chicago from Seattle. Lane is actually in the air. 561 01:08:23.640 --> 01:08:29.579 So, but, you know how long I have to wait a few arise before me then the way it is for me is Darryl. 562 01:08:29.579 --> 01:08:33.119 Or, but otherwise the way it is continuous. 563 01:08:33.119 --> 01:08:42.210 More fun things typical exponential distribution. We'll get into this more later. This is nice because the time. 564 01:08:42.210 --> 01:08:47.909 Until you succeed as independently of how long it's been happening radioactive decay. 565 01:08:47.909 --> 01:08:54.960 2 dimensional things points, falling in squares. This is a nice way to motivate these. 566 01:08:56.159 --> 01:08:59.460 Who variable continuous distributions. 567 01:08:59.460 --> 01:09:02.609 So, okay, so. 568 01:09:02.609 --> 01:09:05.970 I found watching the snow. 569 01:09:05.970 --> 01:09:09.960 Other than that and. 570 01:09:11.550 --> 01:09:22.020 Right no, Lemme get unlimited money would lose well, it's in a philosophical argument and do about this Petersburg paradox. People can look it up. 571 01:09:24.954 --> 01:09:38.965 Eva. 572 01:09:42.479 --> 01:09:48.449 Yeah, or newly is a famous person or probability so. 573 01:09:48.449 --> 01:09:52.439 You could talk about today and we turn on the mathematics. 574 01:09:52.439 --> 01:10:02.970 Yeah, so you can have fun with this and read them. There's piles of people that philosophers argue about that. So. 575 01:10:04.199 --> 01:10:12.510 Okay, sort of like the Xeno paradox. Okay, so so these other questions, then quest away. 576 01:10:12.510 --> 01:10:16.560 Otherwise, I'll see you on Thursday. 577 01:10:34.739 --> 01:10:48.989 No questions, where do we access the grade scope for this class if you were registered by a week ago I added you otherwise, send me email. 578 01:10:58.050 --> 01:11:04.920 Um, professor, can you hear me? Yes, yes. Okay. When when is the office hour for this class? 579 01:11:04.920 --> 01:11:18.329 Office hours I haven't set them up. Yet. I'm wait around after class. Other than that. I'll put up the ta's emails and well, I think I already did and you can email the and so on. 580 01:11:18.329 --> 01:11:27.300 Was being virtual things I didn't think it was important. So important has specific times, but if you'd like that, I'll set them up. So. 581 01:11:27.300 --> 01:11:31.920 Email me to remind me no. 582 01:11:31.920 --> 01:11:39.930 Okay, and I, I'm having some problems with the homework of the last question. So can I ask you now or. 583 01:11:39.930 --> 01:11:45.449 Yeah, you ask me now a quick question. Sure. What's the question? 584 01:11:45.449 --> 01:11:49.710 Yeah, just the last question about the homework. 585 01:11:49.710 --> 01:11:54.510 I can't remember what it is now. 586 01:12:01.560 --> 01:12:07.199 It's all describing the. 587 01:12:07.199 --> 01:12:16.619 Right, I mean, like the main sample me and the voltage of the 7. okay, this is here actually exercise 110 you mean. 588 01:12:16.619 --> 01:12:22.079 Oh, yeah, yeah. Okay. Just a 2nd here. Um. 589 01:12:22.079 --> 01:12:25.739 On page 22nd. 590 01:12:53.609 --> 01:12:58.890 Okay, um, what I would do there. 591 01:13:00.569 --> 01:13:07.829 I haven't defined mean yet, so maybe I shouldn't have asked the question yet, but you'd integrate the. 592 01:13:09.869 --> 01:13:16.050 I would just integrate it and see what the mean is. So. 593 01:13:16.050 --> 01:13:22.170 Um, yeah, but you're also just look at it. 594 01:13:22.170 --> 01:13:32.310 I've done problem a, and B, I'm just okay. See, because, uh, I, I have no idea what. Oh, okay. See, um, every child seconds. 595 01:13:32.310 --> 01:13:36.029 Yeah, cause when when tell is. 596 01:13:36.029 --> 01:13:40.199 For a whole, a whole tier it it it might be. 597 01:13:40.199 --> 01:13:52.770 Had a very strange answer. So well, that's the correct answer. In fact, if you sample ones recycle at the top, it's gonna be high. If you sample once per cycle at the bottom, it's gonna be low. 598 01:13:53.970 --> 01:13:57.239 Yeah, that would yeah, correct. That would be the correct answer. In fact. 599 01:13:57.239 --> 01:14:08.069 So and what if the tower is not appear it it's for instance, uh, point while we're point to what, what will it be. 600 01:14:08.069 --> 01:14:16.140 Well, it would depend if point 1 exactly. Divides the period. 601 01:14:16.140 --> 01:14:19.319 And that case, you know, the. 602 01:14:19.319 --> 01:14:31.949 The shift, which sort it would slightly affect the answer if it did not exactly divide the period, then it would average out to 0T, but we're getting way beyond the course here. 603 01:14:31.949 --> 01:14:36.569 Um, so but. 604 01:14:36.569 --> 01:14:44.220 You know, if you sampled probably doesn't have a big if you sample, like, twice per period. 605 01:14:44.220 --> 01:14:48.420 And well, it's going to average out to 0. 606 01:14:50.220 --> 01:14:56.460 So, I'm thinking it probably. 607 01:14:56.460 --> 01:14:59.970 Averages out to 0T if it's. 608 01:15:00.989 --> 01:15:10.590 More than the period egg, this is actually related to things like in video signal process thing and so on. 609 01:15:10.590 --> 01:15:22.800 And you get into aliases questions, like an old movies, the spokes in a wagon wheel would a political slowly go backwards or something? And because the camera is sampling. 610 01:15:22.800 --> 01:15:28.140 Yeah, yeah, I know that. So, yeah, it will also be 0T or. 611 01:15:28.140 --> 01:15:33.539 Yeah, I'm thinking it's 0T and you just have to you're getting deeper than the course requires. So. 612 01:15:33.539 --> 01:15:38.850 Oh, okay. Thank you. It's intended to make you think. 613 01:15:38.850 --> 01:15:43.229 Oh, yeah. 614 01:15:43.229 --> 01:15:58.109 Okay, anyone else have question yes. Question away. Yeah. So I was out for a lecture. So can you post the recordings somewhere where I can access them? Or should I email you about them? 615 01:15:58.109 --> 01:16:03.720 They are on well, because I checked the website and it didn't see him. 616 01:16:03.720 --> 01:16:16.739 Okay, if you go to media site, um, let's see. What's that? Okay RPI has this video processing thing. It's a really funny. 617 01:16:17.760 --> 01:16:26.039 We try and find it. Um, yeah, email me to remind me, but what I'm going to do is try to find it. 618 01:16:26.039 --> 01:16:31.619 This is not it and post it for you right now. 619 01:16:31.619 --> 01:16:36.180 Maybe you do, where do you site things. 620 01:16:36.180 --> 01:16:40.380 Come on. 621 01:16:43.470 --> 01:16:56.460 Let's go there we go. 622 01:17:08.939 --> 01:17:16.890 Here, okay, well. 623 01:17:16.890 --> 01:17:20.909 How to do a demo for class and it doesn't. 624 01:17:20.909 --> 01:17:28.109 Oh, okay, good. Okay. And here we have engineering probability. 625 01:17:28.109 --> 01:17:37.409 Last 1, in class 2, and it got to keep sending that up and here it is for Thursday. 626 01:17:37.409 --> 01:17:43.739 No, um. 627 01:17:44.880 --> 01:17:48.569 So, yeah, okay. I'm, I'm not. 628 01:17:48.569 --> 01:17:53.460 Fair the application again. 629 01:17:53.460 --> 01:18:00.479 Okay, so if you're seeing it. 630 01:18:00.479 --> 01:18:05.010 You are our media site? Not that. 631 01:18:05.010 --> 01:18:09.779 And let me, let me try to. 632 01:18:09.779 --> 01:18:13.979 See, if I can get. 633 01:18:20.010 --> 01:18:28.439 Okay, something like that will work our start trimming trailing things off and you'll, you'll see the real. 634 01:18:28.439 --> 01:18:41.725 You'll see. Okay. Yeah. Do you think you could drop that link that you have right there? Because I tried media site and the messed up you and I take me some Microsoft page right? Well, you have to add media site 5, remind media site or something. 635 01:18:41.725 --> 01:18:55.135 Don't ask me why I'll put this on the web. I'll put this on the blog so okay. Thank you. You're welcome. And if you go to the here, the transcripts, if you go up to the top files. 636 01:18:55.439 --> 01:19:01.020 So there is the transcripts for what they're worth create done by Webex. 637 01:19:01.020 --> 01:19:08.069 And there are there and written handwritten things to save anything non trivial. 638 01:19:08.069 --> 01:19:11.460 Um, and so on. 639 01:19:11.460 --> 01:19:16.649 And the chat thing, if there's anything non trivial, so. 640 01:19:16.649 --> 01:19:21.300 And that's all. 641 01:19:21.300 --> 01:19:24.600 Here in the files. 642 01:19:24.600 --> 01:19:30.479 Okay, yes, thank you. You're welcome up here. Our files. Okay. 643 01:19:30.479 --> 01:19:35.430 Other questions. 644 01:19:35.430 --> 01:19:42.060 Okay. 645 01:19:48.479 --> 01:19:54.930 Okay. 646 01:19:57.600 --> 01:20:03.180 Okay, then in that case, let's see everyone on. Um. 647 01:20:04.380 --> 01:20:06.149 Thursday.