WEBVTT 1 00:01:13.469 --> 00:01:45.540 Silence. 2 00:02:05.040 --> 00:02:15.599 Okay, good afternoon. Everyone. 3 00:02:16.949 --> 00:02:21.389 And. 4 00:02:22.164 --> 00:02:36.895 So this is probably Becky 2500 the 1st class John 25th Thank you John package account. Great. So, I'm attempting to share my screen. Can you see on the right half of your screen? 5 00:02:38.340 --> 00:02:42.240 The blog or not you can thank you. 6 00:02:42.240 --> 00:02:46.740 Right, because I you see, I can't actually see what you're seeing. 7 00:02:46.740 --> 00:02:51.689 So, I'm attempting to have the chat window open. 8 00:02:51.689 --> 00:02:54.750 So, if there is a problem. 9 00:02:56.430 --> 00:03:02.759 Put it in the chat window also feel free to ask questions. So. 10 00:03:02.759 --> 00:03:06.150 But also ask questions. 11 00:03:06.150 --> 00:03:09.539 You know, with audio or the chat. 12 00:03:09.539 --> 00:03:17.580 So, I mean, if everyone starts wanting to ask questions immediately that I'll change my mind, but at the moment. 13 00:03:17.580 --> 00:03:22.590 This looks like, excuse me this will work out. Okay. 14 00:03:22.590 --> 00:03:27.509 All right, so 1st of all how do you get. 15 00:03:27.509 --> 00:03:38.430 To the blog excuse me? I've been talking too much today, depending on your browser if you do a Google search for. 16 00:03:41.669 --> 00:05:41.670 Silence. 17 00:07:41.670 --> 00:07:41.790 Okay, 18 00:07:45.925 --> 00:08:56.965 Eva, 19 00:08:56.965 --> 00:08:57.595 can you hear this. 20 00:09:00.479 --> 00:09:08.489 Okay, thank you. Okay, so I'm using the phone and for the audio. 21 00:09:08.489 --> 00:09:12.028 Hey, computers. 22 00:09:13.649 --> 00:09:20.969 Okay, so while I was a 2nd, let me get this so I can see it. 23 00:09:33.658 --> 00:09:38.788 Oh, okay. 24 00:09:38.788 --> 00:09:42.568 Good so. 25 00:09:42.568 --> 00:09:46.918 I can see the chat window we're going through the syllabus. 26 00:09:46.918 --> 00:09:50.068 Description. 27 00:09:52.619 --> 00:09:56.458 Okay, um, of course objectives. 28 00:09:56.458 --> 00:10:01.649 Outcomes we're going to give you some basic math we're going to give you some. 29 00:10:01.649 --> 00:10:04.948 Probability concepts and we're going to. 30 00:10:06.744 --> 00:10:19.524 Give some actual examples and so on, um, I'm the instructor, uh, I've got bachelor's degree from Toronto and pH. D. from Harvard and teaching assistant says Shang, Fernando and men. 31 00:10:19.524 --> 00:10:31.764 Chang and office hours. Well, I'll stay around after class as long as you can, as long as anyone cares to talk to me also. 32 00:10:32.994 --> 00:10:40.974 We'll set up other hours and will set up other hours. So I hope to try and get Webex teams working at some point. 33 00:10:41.484 --> 00:10:56.063 But my, um, the hang up was, I couldn't get teams properly, just sharing my whole screen as I'm doing right now, just with the basic Webex meeting. You're welcome them email me from anywhere. But if you send email from some weird place, it's helpful. 34 00:10:56.063 --> 00:11:02.063 If I know it's coming from someone in course, you can hash tag at Virginia, real name and so on helps. 35 00:11:02.818 --> 00:11:10.318 Okay, computers, I got this course wiki blog, whatever you want to call it and again I showed you how to get at it. 36 00:11:10.318 --> 00:11:17.578 Don't intend to use Piazza because they started charging our a lot of money. 37 00:11:19.109 --> 00:11:26.339 We'll be using grades called too, for you to submit homeworks and I'll add you to grades call for give you a joining code. 38 00:11:26.339 --> 00:11:39.359 Web access some Ford for running profitability examples. I'll be using Matlab and Mathematica many of you have seen Matlab. I mean, if you're an engineer, you really got it. 39 00:11:39.359 --> 00:11:54.323 Get some sense of of some sense of Matlab. It does make her cease insulin. Very well. Mathematica is not a required part of the course, but Mathematica, I'll use later, um, because it does formulas very well. It, um. 40 00:11:57.239 --> 00:12:03.298 The 2nd here right. Do not donate to Piazza. 41 00:12:03.298 --> 00:12:07.408 I will not be using Piazza for this course. So. 42 00:12:09.448 --> 00:12:15.629 And we're not getting enterprise license because we don't think it's worth the money. 43 00:12:17.038 --> 00:12:31.259 Okay, and they were free for the 1st, 2 years or so then they started going up. Okay keep the messages coming. Okay. Mathematica will work with equations and formulas. 44 00:12:31.259 --> 00:12:39.479 So that I'll be demonstrating it later, you're welcome to play with it. You're not required to won't affect your grade textbooks. 45 00:12:39.479 --> 00:12:42.629 Okay, the on Garcia. 46 00:12:42.629 --> 00:12:48.418 It is an excellent textbook, except for 1 thing, which is the price. 47 00:12:48.418 --> 00:12:59.399 What's the keep increasing every year? The thing is that everyone uses the book, you know, different colleges. It has many many examples on works and so on. 48 00:12:59.399 --> 00:13:03.778 So, apart from the price, that's actually a good book. So. 49 00:13:03.778 --> 00:13:07.528 You know, the least worst example. So that's what we. 50 00:13:07.528 --> 00:13:13.259 That's what I'll be using a lot of web material and probability also. 51 00:13:13.259 --> 00:13:19.619 Um, which is quite good by the way if my sound quality. 52 00:13:19.619 --> 00:13:25.109 Gets too bad. Let me know, and I can go and get a headset. It's just that I didn't want to, you know. 53 00:13:25.109 --> 00:13:28.948 Make people wait while I ran and got the headset so. 54 00:13:28.948 --> 00:13:42.058 So, if this works in fine, okay class times and places, the course is all you have the, if you, if you're here, you figured this out, it will be completely virtual. I'm going to lecture live. 55 00:13:42.058 --> 00:13:45.058 With some supplementary videos from. 56 00:13:45.058 --> 00:13:51.688 And so on, you're welcome to ask questions with chat maybe even with audio attempt to save the chat window. 57 00:13:51.688 --> 00:13:56.428 But it won't always, um, it won't always work, but I will try. 58 00:13:56.634 --> 00:14:04.614 Also, I'll try to save the video, the video of the class also, and upload it to media site. 59 00:14:05.183 --> 00:14:12.114 So I understand we have some students from China and places that are many time zones away like, 12. 60 00:14:12.359 --> 00:14:21.714 So, I'm working to work with you, you do not have to get up in the middle of the night. There will be no in class quizzes for points and sauna may ask some things without point. 61 00:14:22.283 --> 00:14:28.313 But you do not have to watch the class live because I'm going to try to record everything. 62 00:14:28.619 --> 00:14:39.058 And, um, so you can watch it at your leisure also in this class blog wiki, whatever you want to call it. I will. 63 00:14:39.058 --> 00:14:43.979 Try to briefly summarize everything like I have right here so. 64 00:14:43.979 --> 00:14:52.708 The only thing is last fall, 10% of the media site attempts failed. So, but if I just check right now, just for fun. 65 00:14:52.708 --> 00:14:57.298 We are recording good. 66 00:14:57.298 --> 00:15:04.769 Okay, if I sounds cynical about computers as well. 67 00:15:04.769 --> 00:15:19.678 Okay, Blackboards didn't have that problem. Okay. Getting serious now. Um, so there's no in class attendance if I have an in class quiz or something, it will not be graded. It'll just be a chance for me to evaluate myself. 68 00:15:19.678 --> 00:15:26.849 About whether things are working, um, to, to do exams are going to worry about later. 69 00:15:26.849 --> 00:15:30.028 I try to have 3 exams. 70 00:15:30.028 --> 00:15:34.739 Putting in the final now, the thing is, if you go. 71 00:15:34.739 --> 00:15:47.548 I would hope you wouldn't abuse this a synchronous thing too much. If you're taking this at the same time as an economics course or something. And probability is your major major is. 72 00:15:47.548 --> 00:15:53.548 That I would hope you would treat the profitability course more seriously than your economics. Course for example. 73 00:15:54.354 --> 00:16:08.783 We tried to set the time for this course to minimize conflicts with other classes. There's still a conflict. If you abuse the recommended course sequence badly enough, you can create a conflict, but we did try to optimize that. 74 00:16:09.119 --> 00:16:12.749 I won't schedule anything outside of classes, so. 75 00:16:12.749 --> 00:16:19.318 And you're welcome interrupt the class with questions and so on. 76 00:16:19.318 --> 00:16:31.078 Okay, great. We'll have exams. I'll put dates up in a day or 2. um, again understanding we have some students from China. Um. 77 00:16:31.078 --> 00:16:37.828 We'll have to think of something reasonable for the exams, because it's not fair to make you wake up in the middle of the night. 78 00:16:37.828 --> 00:16:42.599 Okay, and you can skip the final. I feel like it 1st, 2 grade. So gonna have lots of homework. 79 00:16:42.599 --> 00:16:48.899 Makes many of them small and submit them on grade scope. We prefer to get them on time. 80 00:16:48.899 --> 00:16:55.649 And both answers, and some of the homework questions will get recycled this exam questions. 81 00:16:55.649 --> 00:16:59.519 The lowest 1 if you. 82 00:16:59.519 --> 00:17:04.378 It gives me useful extra information or you catch me out in an error. 83 00:17:04.378 --> 00:17:10.199 Um, you might get extra points so if you post an interesting thing, I, I think. 84 00:18:27.209 --> 00:18:37.798 Okay, that's good. Good. Good. Thank you. 85 00:18:37.798 --> 00:18:42.269 I hope it's not going to keep cutting out every 20 minutes throughout the whole. 86 00:18:42.269 --> 00:18:48.808 Dang, but okay, you know, at all points you put what's interesting stuff. You get extra points. 87 00:18:48.808 --> 00:18:57.209 And wait, you can read this and homework. They're all going to be out of different numbers of points but computers can do division. 88 00:18:57.209 --> 00:19:02.608 And so we'll normalize each homework to be the same way cut off. 89 00:19:02.608 --> 00:19:08.308 And if you disagree, great scope is a nice way to report. 90 00:19:08.308 --> 00:19:13.769 Protests about grades and you've got to do it in a timely way. Like, not at the end of the semester. 91 00:19:14.788 --> 00:19:20.669 We're going to give you, and if you feel that something's unfair, you can go. 92 00:19:20.669 --> 00:19:25.469 You know, well, grading teaching assistant will be doing the grading. So, you. 93 00:19:25.469 --> 00:19:30.898 They'll look at your appeal if you don't like that. Look go to me, you can always go to another profit in the department. 94 00:19:30.898 --> 00:19:37.828 Or, to professor, Lou, has the undergrad had, or to professor had and so on. 95 00:19:37.828 --> 00:19:42.959 Give you a mid semester assessment, or maybe even more often. I'm not certain. 96 00:19:42.959 --> 00:19:46.739 There's an early warning system you can post notes about, you. 97 00:19:46.739 --> 00:19:52.229 You're all aware of that academic integrity. 98 00:19:52.229 --> 00:19:59.338 The relevant things is, you're welcome to color. Okay. You can do the homework in teams and I say how big a team can be. 99 00:19:59.338 --> 00:20:05.939 You cannot do the exam and teams, um, homeworks, you're welcome to collaborate with other. 100 00:20:05.939 --> 00:20:10.318 Teams on your homework, but you got to write it up yourself. 101 00:20:10.318 --> 00:20:18.868 You're welcome to do research, but you have to write up the answer yourself and, you know, 2 teams don't hand in the same homework or something. 102 00:20:18.868 --> 00:20:32.308 You're also welcome to get assistance in writing and stuff like that. Just have to acknowledge it. So if English, perhaps that's not your 1st language then you're welcome to get writing assistance from someone. 103 00:20:32.308 --> 00:20:37.318 Who is the English speaker, but it's presumably not helping it was probability. 104 00:20:37.318 --> 00:20:43.019 What do you acknowledge? The exams aren't gonna be an honor system. 105 00:20:43.019 --> 00:20:51.028 Don't get information is other rules. You've seen just assume that I type them in here. 106 00:20:51.028 --> 00:20:55.439 Feedback again. 107 00:20:55.439 --> 00:21:09.719 I like probability, I asked to be given this course, and took a few years before they gave it to me. I'm glad they did 1 reason. I like it is, I can have so many cool, real world examples and I'll show you some of them in every class. 108 00:21:09.719 --> 00:21:15.509 Okay questions on that. 109 00:21:25.558 --> 00:21:29.669 Well, if you think of questions in a minute or so, and again, if I'm. 110 00:21:29.669 --> 00:21:35.878 My soundness to Monday, let me know. Okay. Syllabus. 111 00:21:35.878 --> 00:21:42.179 What I like to do now is give you some real world examples. 112 00:21:42.179 --> 00:21:45.209 Will there be a lab. 113 00:21:50.038 --> 00:21:54.449 I am. 114 00:21:55.558 --> 00:21:55.979 Yeah. 115 00:22:14.759 --> 00:22:24.028 Okay, um, so here's some real world examples and let me. 116 00:22:24.028 --> 00:22:27.179 Just a 2nd, on. 117 00:22:37.378 --> 00:22:42.719 Hello. 118 00:22:43.949 --> 00:22:48.898 Just want to start the webcam, I mean, and hope it doesn't. 119 00:22:49.374 --> 00:22:50.394 Kill everything else. 120 00:23:09.989 --> 00:23:13.439 I'm not going to start the webcam a 2nd. 121 00:23:40.409 --> 00:23:44.638 Okay is not working let's try this. 122 00:23:44.638 --> 00:23:49.679 I mean, let's assume that we have a. 123 00:23:59.009 --> 00:24:03.209 Okay, there's a phone line, we've got various users, um. 124 00:24:16.378 --> 00:24:19.769 Okay, and here is something like. 125 00:24:19.769 --> 00:24:28.588 Or something okay. 126 00:24:28.588 --> 00:24:38.278 So, we've got all these users on the phone line and the question is maybe or a buy assigned home here and fortunate enough to have us. 127 00:24:38.278 --> 00:24:45.628 Fiber optic, and and let's say t t or rise and has said that each user. 128 00:24:45.628 --> 00:24:51.058 Could have all 300 megabits a 2nd speed or something. 129 00:24:51.058 --> 00:24:54.239 So, let's suppose there are a 1000 users. 130 00:24:54.239 --> 00:25:06.058 So, 200 megabits a 2nd, times a 1000 if each user got the 300 megabits, the 2nd, then that line would have to 300 gigabits. The 2nd speed. 131 00:25:06.058 --> 00:25:12.239 But I can't, he's not going to do that. That's too expensive. So, at T is going to. 132 00:25:13.378 --> 00:25:18.239 You know, use some probability and I talk about it so much. 133 00:25:18.239 --> 00:25:23.578 Here, okay, can keep our eyes and or whatever and maybe. 134 00:25:26.068 --> 00:25:31.949 You know, they're going to assume maybe user has a. 135 00:25:31.949 --> 00:25:34.949 1% chance of being on the. 136 00:25:34.949 --> 00:25:42.028 Using that simultaneously you can argue about is that correct? And they're going to the probability that they cannot provide the service. 137 00:25:42.028 --> 00:25:47.219 And so there's a lot of money riding on this because if they install. 138 00:25:47.219 --> 00:25:53.608 Too big a channel, they're paying money if they install to small a channel, then. 139 00:25:53.608 --> 00:25:58.888 I'm going to have to satisfy customers who might jump over to specter. 140 00:25:58.888 --> 00:26:07.019 Spectrum sorry well, no, I mean, they can't, they can't be so bad that people are gonna jump over to spectrum. Um, but you got the idea. 141 00:26:07.019 --> 00:26:18.449 Well, maybe they could be that bad, but okay, so anything, um, roads, um, if you drive up to Clifton park, say, 5 PM on a weekday at the twin bridges is going to be a traffic jam. 142 00:26:18.449 --> 00:26:25.439 So, why don't they so they can calculate probabilities and so it's a probability tool for that sort of stuff. 143 00:26:25.439 --> 00:26:31.348 Life insurance that you pay your money while you're alive and then. 144 00:26:31.348 --> 00:26:36.028 Your estate gets money when you die. So how long will you live before you die? 145 00:26:36.028 --> 00:26:40.048 Probability or 2nd thing is what's the probability you might. 146 00:26:40.048 --> 00:26:44.939 Dropped the insurance plan before you collect so, um, you know. 147 00:26:44.939 --> 00:26:50.128 Maybe you can't afford the premiums or whatever you get set up with that. So. 148 00:26:50.128 --> 00:26:54.898 If you drop the plan before you die, it's pure profit for the company. So they might want to compute that. 149 00:26:54.898 --> 00:26:59.278 Pension plans are in the news now with budgets so got the probability. 150 00:27:01.074 --> 00:27:15.233 Again, the people living to 100 years old profitability is the stock market doing different things, because they've invested assets in the stock market. It's social security. There is the social security benefits or index to inflation. All these things have probability. 151 00:27:15.233 --> 00:27:17.663 There's a lot of money riding on doing this. 152 00:27:18.358 --> 00:27:24.358 Or, maybe, um, Tesla, you notice, I typed up this example. 153 00:27:24.358 --> 00:27:36.989 In a little while ago, uh, actually 2 years ago and then test. So it was 478 since then of course, it's slipped what, 5 to 1. so it's gone up by a factor of 10 or something. 154 00:27:36.989 --> 00:27:41.519 So you want to a typing error there. 155 00:27:41.519 --> 00:27:52.169 So you want to again, there's money involved in getting the probability, right? You want to say, by not an option the test will be 20% more. 156 00:27:52.169 --> 00:27:57.328 In 6 months, what's the fair price for the option? So that's why probability is useful. 157 00:27:57.328 --> 00:28:03.838 Now, any of these things involve modeling. 158 00:28:04.253 --> 00:28:12.354 And because you're modeling something that occurs in the future, for example, you want to model life expectancies. 159 00:28:12.354 --> 00:28:20.153 Some latest thing with cobit 19, is that has produced us life expectancy by 1 full year. 160 00:28:20.459 --> 00:28:26.848 So that, you know, we're bringing in probabilities for some of that. 161 00:28:26.848 --> 00:28:32.159 Now, in this course, we'll have models for things like. 162 00:28:32.159 --> 00:28:36.148 Coin tosses and so on. So. 163 00:28:36.148 --> 00:28:41.278 A coin tosses dice and all that sort of thing. 164 00:28:41.278 --> 00:28:47.038 And this is something relevant for modeling, for example. 165 00:28:47.038 --> 00:28:50.278 We'd like to talk about cost coins in this course. 166 00:28:50.278 --> 00:29:01.019 Because it is a simple profitability we assume it'll be 50, 50 heads or tails. So we'll have a model of the real coin. I mean, the real coin has got various types of metal in it. 167 00:29:01.019 --> 00:29:09.509 And, you know, what's the US penny made up today? It's think with a thin coffer coating on it, for example. 168 00:29:09.509 --> 00:29:15.898 And we've had different types of dollar coins at different models and. 169 00:29:15.898 --> 00:29:23.278 But the metals not relevant cause what's important for a model of the coin for this course is it's got a head. It's got a tail. 170 00:29:23.278 --> 00:29:27.088 And it's 50, 50, if you toss it and. 171 00:29:27.088 --> 00:29:32.909 If you tossed the coin twice, the 2 passes are not related to each other. 172 00:29:32.909 --> 00:29:37.469 It comes up heads the 1st time. It's not. 173 00:29:37.469 --> 00:29:43.888 It'll still be 50, 50 on the 2nd, 1 independently. If I talk to clients at the same time, they won't. 174 00:29:43.888 --> 00:29:49.108 Be related to each other, so these are things about the models so. 175 00:29:49.108 --> 00:29:57.898 You know, we have this simple model in the course heads entail 50, 50, that ignores all this irrelevant stuff. But what the coins made off. 176 00:29:57.898 --> 00:30:03.148 This is the relevant thing that the policies again aren't don't affect each other. 177 00:30:03.148 --> 00:30:07.679 Now, we capture the relevant and we ignore the rest. 178 00:30:07.679 --> 00:30:11.699 On the, as I mentioned point 3 a up there. 179 00:30:11.699 --> 00:30:23.219 We model things also that are dangerous and time consuming, not in this course necessary, but you model in aircraft and you test the aircraft model and your simulator to see if it will crash or not. 180 00:30:23.663 --> 00:30:37.673 And because, you know, if you don't mall that you got to build the real plane, which is expensive and takes time. And if it crashes, it kills the test pilot. Probably. So you don't like to do that? Well, that's part of something like you to do that. 181 00:30:37.973 --> 00:30:39.713 Okay, so. 182 00:30:40.019 --> 00:30:49.679 We get things about modeling. We'll use that in this course if we're taught the 6 sided die, the model is it's got 6 phases that come up 6 of the time and. 183 00:30:49.679 --> 00:30:53.939 There's no correlation that mean, there's no relation between 1 toss and another toss. 184 00:30:55.798 --> 00:31:06.598 Okay, so we have models all so you take as a student different type and the systems that we won't use in this course that do modeling, mentioning modeling in general. 185 00:31:06.598 --> 00:31:13.259 So now, so so the models will have probability and. 186 00:31:14.608 --> 00:31:23.068 And other examples, um, say, randomness for profitability. I've got a model. I know you had a fair grounds. 187 00:31:23.068 --> 00:31:31.259 And you're tossing the funny shape basketball until it goes through this small. So, and and when it does you get a price. 188 00:31:31.259 --> 00:31:35.939 Much money let's say, so, the question will be how many times do you have to talk. 189 00:31:35.939 --> 00:31:39.328 The ball to get it into the hooks you got to have a model. 190 00:31:39.328 --> 00:31:42.989 What's the probability of going through the on each task and so on. 191 00:31:44.249 --> 00:31:48.328 Now, Here's a case modeling and probabilities affect. 192 00:31:48.328 --> 00:31:51.959 They come out in public policy also. 193 00:31:51.959 --> 00:31:56.519 Here's an example if you are. 194 00:31:56.519 --> 00:32:00.449 Arrested for a crime, um. 195 00:32:00.449 --> 00:32:06.538 Then various well, now more people are released on bail, but if you're not automatically released on Dale. 196 00:32:06.538 --> 00:32:14.368 Whether or not your release dovetail will depend on a proprietary model of whether you, whether they think you're likely to re, offend. 197 00:32:14.753 --> 00:32:26.723 So, probability comes into that yeah, if you're convicted and then the sentence will depend perhaps on the model of what the justice system thinks you'd like me to do in the future. 198 00:32:27.233 --> 00:32:29.874 So probability comes into public policy. 199 00:32:34.558 --> 00:32:38.818 Like, to talk about some different types of models here. 200 00:32:38.818 --> 00:32:43.318 Um, there's deterministic models, like, if you've got to resist or. 201 00:32:43.318 --> 00:32:47.308 You know, vehicles, if it's a 1000 Resistor. 202 00:32:47.308 --> 00:32:52.078 And I have 1 vault across it, then there will be 1M, throw it. 203 00:32:52.078 --> 00:32:56.128 Nice and simple nice and linear some limitations. 204 00:32:56.128 --> 00:33:03.419 You know, if, um, if I put 10000 volts across the resist there. 205 00:33:03.419 --> 00:33:09.568 I will not get 10 AMS through it because 10000 volts resistor might explode. It might not. 206 00:33:09.568 --> 00:33:17.338 Take that voltage if I put a micro Volt across the resist, or I might not get a Nano amp through it because. 207 00:33:17.338 --> 00:33:22.108 We're going to get some other effect, noise effect or something. So, the point about. 208 00:33:22.108 --> 00:33:25.259 5.6 here is that. 209 00:33:25.259 --> 00:33:30.088 Models of limitations, um, just a 2nd. 210 00:33:32.128 --> 00:33:35.969 So, um. 211 00:33:35.969 --> 00:33:42.239 Also, if I put say, a jigger Hertz signal through the resist there. 212 00:33:42.239 --> 00:33:51.749 I might discover that has gotten autosomal impedance for capacitance. So things have limits but apart from that, the resistance, the deterministic model vehicles. 213 00:33:51.749 --> 00:33:56.009 Um, just probabilistic models if I hadn't reelect, we'll. 214 00:33:56.009 --> 00:33:59.608 Then and assume it's got 38 slots. 215 00:33:59.608 --> 00:34:14.338 Numbers 1, through 36 and a 0T and double 0T, then I might assume that each the ball will fall in each spot 38 of the time and it's independent of the different tosses and so on. That'd be a probabilistic model. 216 00:34:14.338 --> 00:34:20.639 Of course, um, fun things like this. Um. 217 00:34:23.219 --> 00:34:28.679 This was some MIT students who were able to model reelect wheels actually. 218 00:34:28.679 --> 00:34:32.639 Okay. 219 00:34:34.018 --> 00:34:42.989 Sometime I'll tell you about when MIT students legally cracked the Massachusetts numbers game. 220 00:34:42.989 --> 00:34:50.429 And found that a couple of times of the year, the expectation went positive. And if they bet they would make a small profit. 221 00:34:50.429 --> 00:34:59.728 So, they set up syndicates of people to to buy tickets in those cases and they bought, I don't know, half of all the tickets sold in the whole state. 222 00:34:59.728 --> 00:35:04.648 And made some money, and they were investigated by the state. 223 00:35:04.648 --> 00:35:09.809 The relative report, which is publicly available and send me your later. We said they were legal. 224 00:35:09.809 --> 00:35:13.889 However, later they changed the Massachusetts changed the rules. 225 00:35:13.889 --> 00:35:17.128 Oh, okay. Any case you got models there and so. 226 00:35:18.539 --> 00:35:27.599 Um, okay points about Here's a quick introduction and professor Rad key. 227 00:35:28.648 --> 00:35:41.369 His, but I haven't met, I'm going to anticipate a little I want you to watch, um, retract key some videos, which we'll talk about this and he'll be drawing influences. So just a quick summary here. 228 00:35:41.369 --> 00:35:44.878 We got random experiments like you're tossing, you're. 229 00:35:44.878 --> 00:35:50.219 Coin, um, could be a header tale each time and outcome. 230 00:35:51.449 --> 00:35:56.969 An outcomes ahead a different outcome is a tale. The possible outcomes are heads and tails. 231 00:35:56.969 --> 00:36:00.208 So, if my. 232 00:36:00.208 --> 00:36:04.318 Pam, we're working, I'd be drawing this for you. 233 00:36:04.318 --> 00:36:10.768 In case, they've got the possible outcomes and I'll, I'll get this more in detail later, but basically. 234 00:36:10.768 --> 00:36:18.478 And Chris, he mentioned, we've got some various terms here for outcomes and experiments and so on. 235 00:36:19.528 --> 00:36:23.309 So, I'll come back to that in more detail later. 236 00:36:23.309 --> 00:36:26.789 Now, in the course. 237 00:36:26.789 --> 00:36:32.159 Whereas filming that say that we talked the coin, and it comes up heads or tails. 238 00:36:32.159 --> 00:36:36.599 If I toss it 10 times, I'm like, it's 7 heads and 3 tales. 239 00:36:36.599 --> 00:36:43.648 That's not 50, 50, but it could happen at 1 time. In a 1000. if I toss it 10 times, it'll be can heads. 240 00:36:43.648 --> 00:36:49.588 A, no tail, but we assume that eventually things even out. 241 00:36:55.523 --> 00:37:08.963 If I do 10 tosses, I could see 7 heads and 3 tails, but if you do a 1M tosses, I will never see 700000 heads and 300000 tails things have probabilities even out. It's called a lot of large numbers. 242 00:37:10.409 --> 00:37:16.409 Now, there are weird distributions like, something called the coachee distribution that violate this but. 243 00:37:16.409 --> 00:37:22.409 I may not mentioned them that much in this course. So things are regular. 244 00:37:22.409 --> 00:37:30.599 Sort of things you see as examples relative frequency I'll skip next time. 245 00:37:31.679 --> 00:37:40.679 Now, axosomatic approach the significance of this is that. 246 00:37:42.059 --> 00:37:50.724 People like to have some formal rules of what the probabilities are and this way, then they can prove themselves on a little light on that. 247 00:37:51.204 --> 00:37:57.353 But a probability of say, the coin, the probability of had is somewhere between 0T and 1. 248 00:37:57.659 --> 00:38:10.199 And all the different things that can happen, add up to 1. so, maybe it's a bias coin might come up head 60% of the time. But then it will be tales, 40% and 16, plus percent 40% to 1. 249 00:38:10.199 --> 00:38:16.110 So, it's because that entails on occur together. I'm ignoring that. The coin might land on end. 250 00:38:16.110 --> 00:38:24.900 So, and so that's now I want to get specific to talk about, say how you might. 251 00:38:24.900 --> 00:38:29.219 Is probability to build the model. 252 00:38:29.219 --> 00:38:34.800 So we want to model telephone conversations or something, and. 253 00:38:34.800 --> 00:38:47.340 Maybe we assume that the speaker talks a 3rd at the time, perhaps, and listens 2 thirds of the time you got that perhaps maybe your and. 254 00:38:47.340 --> 00:38:58.170 You got that by just looking at your customers, your typical customer, or maybe speak a 3rd of the time listens a 3rd of the time and neither of them say anything. I've heard of the time. Perhaps. 255 00:38:58.525 --> 00:38:59.755 Or this is going, 256 00:38:59.844 --> 00:39:01.405 is that again, 257 00:39:01.795 --> 00:39:03.054 we're the phone company, 258 00:39:03.085 --> 00:39:09.054 and we want to figure out how much how wide a channel we have to provision, 259 00:39:09.085 --> 00:39:09.355 say, 260 00:39:09.355 --> 00:39:11.275 going from the neighborhood to the Central station, 261 00:39:11.275 --> 00:39:14.695 or something or yourself talking about cell phones. 262 00:39:14.695 --> 00:39:21.505 For example, it would be a question of how many cell phone towers you need. Perhaps again, there's money involved here. 263 00:39:21.809 --> 00:39:30.840 Okay, so it doesn't matter. Landline cell phone. The math is the same and to the level of detail I'm doing it. 264 00:39:30.840 --> 00:39:36.599 We've got a lot of customers and we're going to have to assume this is 48 customers. 265 00:39:36.599 --> 00:39:43.230 Out here, and we're going to the point about this is to compute how much um. 266 00:39:43.230 --> 00:39:46.980 Hardware, we need to satisfy the 48 customers. 267 00:39:46.980 --> 00:39:50.010 Okay, or how many channels. 268 00:39:50.010 --> 00:39:55.769 We need, and so to 48 customers, and all of them might want to talk at the same time. 269 00:39:55.769 --> 00:39:59.190 Then you would need 48 channels. 270 00:39:59.190 --> 00:40:03.059 But that's expensive so that. 271 00:40:03.059 --> 00:40:07.949 What we want to do is have fewer than 48 channels and save money. 272 00:40:09.119 --> 00:40:13.289 So, um, and. 273 00:40:13.289 --> 00:40:26.635 You know, and we can simulate things random number generator, computer, random number generator and so on or you could be tossing a dye. And you get 4th does the dye come up 1 or 2? It'll come up 1 or 2 a 3rd at the time. 274 00:40:26.635 --> 00:40:32.965 For example, or you could be picking balls out of an earned probability people like balls and earns because. 275 00:40:33.869 --> 00:40:38.579 Very easy to talk about and so on. Okay. 276 00:40:38.579 --> 00:40:43.769 So, the problem is, we've got 48 customers of the phone company. 277 00:40:43.769 --> 00:40:50.639 And the question is, how many channels that we have to have to, to satisfy them. 278 00:40:51.204 --> 00:41:05.425 Um, and maybe we're talking about packets that are hundreds of a 2nd, each packet, a 3rd of the customers a 3rd of the we'll be talking. Okay. So, on the average, you need a 48 times the 3rd, that would be 16 channels. 279 00:41:06.420 --> 00:41:10.980 Okay on the average 38 channels, 16 channels are needed. 280 00:41:10.980 --> 00:41:22.590 But here's the problem that, um, if you just have 16 channels, a good fraction of the time, like, half the time, There'll be more than 16 customers trying to talk. 281 00:41:22.590 --> 00:41:30.269 And it's extra customers, like, you're gonna be discarding the packets and what they say is kind of get dropped and it might get annoyed. 282 00:41:30.269 --> 00:41:42.000 So, and I'm guessing if you have all these 16 channels, although that's the average that you need about half the time, you're going to be dropping, at least 1 customer, and maybe dropping several customers. 283 00:41:42.000 --> 00:41:45.869 So, 48 customers, 48 channels. 284 00:41:45.869 --> 00:41:55.440 It's wasteful cause it'd be almost never all 48 customers be talking at the same time. It'll be like, 100 to 48 or something. 285 00:41:56.514 --> 00:42:02.605 That's not exactly right. You get the idea if we had the 6, but the expected number of channels used is on the average. 286 00:42:02.635 --> 00:42:12.264 Haven't told you what expected means, but a 3rd of the customers are talking at a time, 48 customers on the average, or haven't defined average 16 channels will be needed but that's too few. 287 00:42:13.230 --> 00:42:18.030 There's a lot of the time, this is more than 16. 288 00:42:18.030 --> 00:42:23.880 So, what we want to do is throw mathematics status, which I'll do it later. 289 00:42:23.880 --> 00:42:29.250 And let's assume that it well, if a people talked and a like, a random variable. 290 00:42:29.250 --> 00:42:32.369 If a bigger than, um. 291 00:42:32.369 --> 00:42:38.760 The number of channels out that we've allocated that we thought were gonna have to discard a minus M packet. 292 00:42:38.760 --> 00:42:46.949 So, if we bought only 16 channels, and 20 people tried to talk 4, people are going to have the voice. 293 00:42:46.949 --> 00:42:54.900 Dropped so now, what we can do, you you can see is we can track the expected number of people of customers. 294 00:42:54.900 --> 00:42:58.619 Who are getting parts of the conversation dropped you say. 295 00:43:00.300 --> 00:43:04.710 And we could simulate it there. We could do math at it. And, um. 296 00:43:07.679 --> 00:43:12.360 We could do something like here um, we could talk about. 297 00:43:13.619 --> 00:43:18.300 If we try it and we could to simulate it also if you don't want to do the math. 298 00:43:18.300 --> 00:43:21.900 Again, random number generator and we might do a. 299 00:43:21.900 --> 00:43:26.400 A 1000 trials, maybe and of those 1000 trial. 300 00:43:26.400 --> 00:43:32.130 Little ends with a 1000 then how many of those try? How many of those trials. 301 00:43:32.130 --> 00:43:40.320 Do we need 16 packets 18 packets 20 packets whatever. 302 00:43:40.320 --> 00:43:44.550 That 20 packets, because 20 customers wanted to talk at the same time. 303 00:43:44.550 --> 00:43:47.789 Well, we can. 304 00:43:47.789 --> 00:43:52.710 Like I said, we can just look at our 1000 trials and just add up. 305 00:43:52.710 --> 00:44:01.920 We don't need it. We're not using any maps, so I'll actually we can get the exact form something called for sponsors. We still get it later, but you see what I can do down here. 306 00:44:01.920 --> 00:44:05.130 Is I'm adding up, um. 307 00:44:05.130 --> 00:44:13.769 Basically was the number the average number of packets that are sent and that's the expected value of a. 308 00:44:13.769 --> 00:44:20.519 And then we can use that, compare that to the number of channels we bought and work out. How many happy customers. 309 00:44:21.630 --> 00:44:25.920 So this is an example of probability with a packet transmission. 310 00:44:25.920 --> 00:44:30.659 Real World probability. I'd like to give you another example now. 311 00:44:30.659 --> 00:44:38.550 And we have an unreliable communications channel, and we're transmitting. 312 00:44:38.550 --> 00:44:52.585 An image or something that'd be a black and white facsimile scan and we're transmitting zeroes are 1 each sequence a bit that is there or 1 or we just took anything and converted to binary representation zeros the ones. 313 00:44:53.065 --> 00:44:54.893 So we're reading zeros and ones. 314 00:44:55.170 --> 00:45:03.449 And we're receiving zeros are ones. 315 00:45:03.449 --> 00:45:07.289 But 1st, were there any questions about the, um. 316 00:45:07.289 --> 00:45:10.710 Provisioning like the cell phone thing, the number of champ. 317 00:45:10.710 --> 00:45:18.690 Okay, so unreliable communications channel. The thing is, when we transmit is 010% of the time. 318 00:45:18.690 --> 00:45:26.429 It gets received as a 1, and if we transmit 120% of the time, it gets received as a 0. 319 00:45:26.429 --> 00:45:37.380 And zeros and ones are not being transmitted at the same right? Like, if we scan paper and 0T is white, and 1 is black, 99% of the bits will be 0. 320 00:45:37.380 --> 00:45:43.409 So, now you may be ahead of me now so we receive a 0T what was transmitted. 321 00:45:43.409 --> 00:45:49.440 What was the, what's the problem if we receive as 0T? What's the probability of? The 0T was transmitted. 322 00:45:49.440 --> 00:45:55.920 Little math involved here you see, I even probably work it out, but you'd have to think a little, um. 323 00:45:55.920 --> 00:46:10.164 Because if we try the thing is, if we go from the transmitted, and we transmit a 090% of the time, it's received visit 0T. If we translate a 120% of the time, it's received 0T. But from the receiving end, we have to sort of now invert this. 324 00:46:10.164 --> 00:46:17.605 And figure out what was the probability that a 0T was transmitted, bringing in the package zeroes and ones are not transmitted with the same profitability. 325 00:46:19.139 --> 00:46:25.860 So this is important because we want to design the receiver. So it does the best guess as to what was transmitted. 326 00:46:27.989 --> 00:46:36.389 Um, unreliable communications channel. Let me give you a 3rd example. 327 00:46:36.389 --> 00:46:42.960 Talking parts, um, back in the day, you know, once upon a time. 328 00:46:42.960 --> 00:46:50.190 Like, a year ago, I actually gave this lecture in person in 1 of the Darren communication center, big rooms, or whatever. 329 00:46:50.190 --> 00:46:55.559 It wasn't big enough for 3, 8, 1 of the ones at the end. Okay. So. 330 00:46:55.559 --> 00:47:01.050 Imagine that we talked about lifetimes of the ceiling bulbs perhaps. 331 00:47:01.050 --> 00:47:05.670 And how many spare parts could you stock that? 332 00:47:05.670 --> 00:47:10.079 You know, there once was a back with incandescent light bulb. 333 00:47:10.079 --> 00:47:14.190 Back in the 1930, so I called manufacturers thoughts together. 334 00:47:14.190 --> 00:47:20.070 And agreed that the lifetime lightbulb should be 1000 hours. This is not an urban legend documented. 335 00:47:20.070 --> 00:47:24.929 Before that there, like, folks lasted longer so basically. 336 00:47:24.929 --> 00:47:32.400 You know, what when the light call gets to be a 1000 hours, should you replace it preemptively? Or how many how many spares could you start? 337 00:47:32.400 --> 00:47:36.809 And, you know, if you buy them. 338 00:47:36.809 --> 00:47:44.070 Too many, and you're paying extra money for your stock that you may not need. If you don't buy enough then the lecture hall. 339 00:47:44.070 --> 00:47:48.389 Is to them, because lights burned out that we couldn't replace. 340 00:47:50.250 --> 00:47:53.699 And let's figure the manufacturer even all. 341 00:47:53.699 --> 00:47:58.769 A lot of products when they manufacture the product and manufacture piles, spare parts. 342 00:47:58.769 --> 00:48:03.210 And, and then change the assembly line and. 343 00:48:03.210 --> 00:48:07.710 If they run out of spare parts, there never will be any more spare parts. So. 344 00:48:07.710 --> 00:48:14.639 A lot of very happy customers who are 3 examples of where profitability is relevant to real life. 345 00:48:16.380 --> 00:48:24.420 Now, got some stuff you can look at on guys see a chapter 1. 346 00:48:24.420 --> 00:48:31.889 Which talks about what I did in more detail also rich red he has some very nice, um. 347 00:48:31.889 --> 00:48:40.590 Bite here and I'd like you to watch the 1st 3 here. 348 00:48:40.590 --> 00:48:44.940 Experiments in the sample spaces and events and so on. 349 00:48:44.940 --> 00:48:48.719 And I'll have you watching about 3 of them for each. 350 00:48:48.719 --> 00:48:53.219 For each class, basically, so you can work ahead on that. 351 00:48:53.425 --> 00:49:02.005 And eventually we'll start having homework questions and then I've got a homework here also in a week. 352 00:49:02.034 --> 00:49:09.655 And to make you think about some of these things number 1 here again, about, for AIS and any reasonable. 353 00:49:10.110 --> 00:49:16.230 And so here, we'll get full points and interesting things. Now, statistics. 354 00:49:16.230 --> 00:49:22.079 I was working with real experiments and real examples. So it's something for you to think about. 355 00:49:22.079 --> 00:49:29.639 And there's questions or causality, just because 2 things are related, doesn't mean that they were. 356 00:49:30.809 --> 00:49:36.659 That 1 of them, cause the other and well, here's an example. I want you to think about historical thing. 357 00:49:36.659 --> 00:49:40.500 back when a lot at one point what half of the adults . 358 00:49:40.500 --> 00:49:45.900 Smoke and about a quarter of smokers died some cancer. 359 00:49:45.900 --> 00:49:50.219 And people said, well, maybe that means if cigarettes are dangerous. 360 00:49:50.219 --> 00:49:54.090 Well, the tobacco companies response was. 361 00:49:54.090 --> 00:50:05.489 Just because the correlation doesn't mean that smoking causes lung cancer, maybe some people are more predisposed to lung cancer. It also makes them fetus opposed to smoke. You know, maybe it went the other way. 362 00:50:05.489 --> 00:50:09.480 Who knows so, the experiments that repaired of that. 363 00:50:09.480 --> 00:50:14.219 And this is an approximation, but what they did is such a thought. 364 00:50:14.219 --> 00:50:20.190 And there's some of the dogs, they force to smoke like, this, these dogs here a smoking. 365 00:50:20.190 --> 00:50:27.510 And some of the dogs are not smoking and the dogs who smoked got cancer quite often. 366 00:50:27.510 --> 00:50:33.329 And the dogs who didn't smoke, never got cancer I guess so that proved that there actually was a causation. 367 00:50:33.329 --> 00:50:41.250 And there's a story here on that, and just some quick example. Okay so this will get you started having some homework questions. 368 00:50:42.809 --> 00:50:47.519 Now, to make things to lighten things up here, um. 369 00:50:47.519 --> 00:50:52.949 Probably built in the real world. The book here called, beat the dealer. 370 00:50:54.210 --> 00:51:00.449 And we talked about ways, you can do better than average and playing blackjack the sales. 371 00:51:00.449 --> 00:51:11.190 Wouldn't necessarily get rich using his methods, but it was interesting. Okay. Probability here. Then later on, went into the stock market and made it. 372 00:51:11.190 --> 00:51:15.239 As you make some money on the stock market, using the same techniques. 373 00:51:19.889 --> 00:51:24.090 Um, and then just the fun. 374 00:51:30.630 --> 00:51:39.750 Yeah, and you can you gotta fun with that. There's quite a few, um. 375 00:51:39.750 --> 00:51:48.750 Are challenged for letting me profitability. Okay so we did today, was had the syllabus and tried to give you a feeling. 376 00:51:48.750 --> 00:51:52.469 And to why probability might be interesting. 377 00:51:52.469 --> 00:51:57.809 And useful in the real world, you're paying money to take this course. So that's, um. 378 00:51:57.809 --> 00:52:02.070 Have you see how it might actually be useful? 379 00:52:04.289 --> 00:52:11.639 So, I'll hang around to, um. 380 00:52:11.639 --> 00:52:20.369 That's enough of stuff for today, I'll hang around if there's any questions we can talk and so questions. 381 00:52:23.429 --> 00:52:27.809 And I'll play with audio a little before Thursday. I don't know audio. 382 00:52:27.809 --> 00:52:33.420 Is this crazy thing I gave another class earlier today and the audio worked fine. 383 00:52:38.579 --> 00:52:43.079 I haven't put up this thing on grades company yet. Yeah. Um. 384 00:52:53.190 --> 00:53:00.090 Give you a homework a week and so on. 385 00:53:13.679 --> 00:53:20.280 Assuming that the link actually works so. 386 00:53:26.250 --> 00:53:33.510 I'll stay around here for a few minutes again. In case anyone thinks of a question other than that. 387 00:53:33.510 --> 00:53:36.659 Have a good week and see you Thursday.