WEBVTT 1 00:00:01.739 --> 00:00:07.860 Well, 1 other person in the meeting. Hi so. 2 00:00:16.439 --> 00:00:27.359 Okay, I'm back to. 3 00:00:27.359 --> 00:00:36.299 So, just to get this on the video, so, this graph of grades X, access versus timeline access, if anything. 4 00:00:36.299 --> 00:00:41.280 It would be slightly negative possibility possibly. 5 00:00:41.280 --> 00:00:44.789 Okay, so. 6 00:00:48.119 --> 00:00:51.359 Just check something for fun. 7 00:00:51.359 --> 00:00:57.810 Okay, now. 8 00:00:57.810 --> 00:01:01.500 New stuff for today. 9 00:01:01.500 --> 00:01:06.299 Are. 10 00:01:06.299 --> 00:01:09.780 So. 11 00:01:09.780 --> 00:01:19.079 I wanted to spend a little too big things for today. I wanted to spend a little time on Matlab. 12 00:01:19.079 --> 00:01:22.319 And some of the stuff it has her probability. 13 00:01:22.319 --> 00:01:27.299 And then have tutorial on probability density because it. 14 00:01:27.299 --> 00:01:31.950 You have to think a little about this to make it work. So, this is actually why I'm. 15 00:01:31.950 --> 00:01:42.329 I'm running off of right running off of my think pad instead of the iPad, because I want to run the Matlab program. 16 00:01:42.329 --> 00:01:48.659 Okay, so this is the blog for today and again, I'll, I'll link in the other thing. 17 00:01:48.659 --> 00:01:52.349 Oh, 1 more thing just a 2nd, here. 18 00:01:52.349 --> 00:01:56.879 Huh. 19 00:01:56.879 --> 00:02:01.200 Come on. 20 00:02:01.200 --> 00:02:04.709 Okay. 21 00:02:11.520 --> 00:02:14.550 Going on here. 22 00:02:14.550 --> 00:02:21.330 Okay. 23 00:02:32.009 --> 00:02:38.759 Okay, good. So, um, so Matlab. 24 00:02:40.020 --> 00:02:48.030 So, I don't know that we used to teach it to all of the undergrads then fell away a little so. 25 00:02:48.030 --> 00:02:54.810 It's a program for working with matrices. There's a lot of functions. It does a lot of engineering things. 26 00:02:54.810 --> 00:03:09.360 Very well, it's a large commercial program. It's very widely used in natural industry and it has dozens also toolkits for specify for special applications, like, control systems and stuff like that. And it's got some stuff in. 27 00:03:09.360 --> 00:03:22.884 For working with profitability, I'll run it. Students have you can download it, you can install it on your computers and so it has a license every connected to our API. The problem is, of course, once you leave. 28 00:03:24.780 --> 00:03:30.150 Then, you know, your company needs a license for it, but any case, I'll show you that. 29 00:03:30.150 --> 00:03:34.530 Um, so. 30 00:03:34.530 --> 00:03:39.780 If you run it for you, where we have it. 31 00:03:41.370 --> 00:03:47.639 Let's see if we can get it to work. 32 00:03:47.639 --> 00:03:53.490 Lab. 33 00:03:57.689 --> 00:04:01.139 Um. 34 00:04:07.919 --> 00:04:20.970 Oh, okay good. So how easy is it to see that you can just want to see it? So, the thing is, it's. 35 00:04:20.970 --> 00:04:24.750 It's an interpretive language it, um. 36 00:04:26.309 --> 00:04:38.488 You type something and you can, you can see it immediately. I could define a variable or something or define an array. Let me see how this might work. 37 00:04:41.519 --> 00:04:46.709 That's a 2 by 2 a matrix and I could say. 38 00:04:46.709 --> 00:04:51.569 And it finds the invert, for example. 39 00:04:55.228 --> 00:05:00.509 And so it works with matrices. 40 00:05:00.509 --> 00:05:04.348 Can work with very large matrices. Um. 41 00:05:04.348 --> 00:05:09.298 And could stay even getting started, there's piles of documentation for it. 42 00:05:09.298 --> 00:05:14.009 And I couldn't bother signing in to get that, but piles of documentation. 43 00:05:14.009 --> 00:05:20.459 And it does various things for probability. 44 00:05:20.459 --> 00:05:30.478 Let me show you right programs in it and so on if you have a parallel computer, you can run on parallel computers. You can write interactive demos. 45 00:05:30.478 --> 00:05:42.718 Stuff like that if it's a compute found thing that engineers use a lot for your transforms. For example, there's going to be something in Matlab, which will do for you transforms fastest had control systems. 46 00:05:42.718 --> 00:05:47.069 Feedback transforms and so on, it will have stuff. 47 00:05:47.069 --> 00:05:52.798 It will have stuff for all of that and I just wanted to see if I could find. 48 00:05:52.798 --> 00:05:56.158 Add ons and so on, um. 49 00:05:59.668 --> 00:06:04.499 Okay. 50 00:06:04.499 --> 00:06:09.569 I don't want to go to the hassle of signing in and so on, but basically it's got a lot of. 51 00:06:09.569 --> 00:06:14.488 A lot of useful things here now, let me show you something specifically for probability. 52 00:06:14.488 --> 00:06:21.119 All right. Okay. Some examples here. 53 00:06:21.119 --> 00:06:27.238 I typed in. Okay and. 54 00:06:27.238 --> 00:06:31.048 It has a lot of built in distributions and. 55 00:06:31.048 --> 00:06:34.588 Do cumulative and probability. 56 00:06:34.588 --> 00:06:38.369 Um. 57 00:06:38.369 --> 00:06:45.269 For example, um, oops, not this 1. 58 00:06:46.829 --> 00:06:52.168 This 1. okay. 59 00:06:57.869 --> 00:07:00.988 So, I can, um. 60 00:07:00.988 --> 00:07:10.439 Well, 1st, some things you can do with this, you can create sequences of numbers. So I could say something like. 61 00:07:12.569 --> 00:07:16.228 Okay. 62 00:07:16.228 --> 00:07:30.928 So, i0, colon 5 and that produced the sequence 012345. I could also do something like 0, say, in steps of point 5 to 5 and that sort of thing. Oops. 63 00:07:30.928 --> 00:07:36.298 Typo that should be. I put it there. We go. 64 00:07:36.298 --> 00:07:44.759 Stuff like that, so, so great sequence and we can work with vectors in many cases as we work with scalers. 65 00:07:44.759 --> 00:07:48.358 For example, um. 66 00:07:48.358 --> 00:07:51.869 I could say vehicle say 0 to 5. 67 00:07:51.869 --> 00:07:59.098 And then I say the time 3, it multiplies each element by 3, for example. 68 00:07:59.098 --> 00:08:04.348 Okay, so probability we could say, say. 69 00:08:05.788 --> 00:08:09.088 Pdf or something. 70 00:08:09.088 --> 00:08:16.348 And we'll get a help and PDF, give it a net. It has a number of built in major probability distribution. I'll say. 71 00:08:16.348 --> 00:08:19.528 Find all meal or something um. 72 00:08:20.879 --> 00:08:23.999 And so I could say, say, PDF. 73 00:08:23.999 --> 00:08:29.158 Give it the name as a string. 74 00:08:29.158 --> 00:08:36.149 I can't spell. I. N, oh, M I. L. I. in there. 75 00:08:36.149 --> 00:08:39.839 Oh, I, uh. 76 00:08:39.839 --> 00:08:43.589 And if I look at my blog here that I typed in. 77 00:08:43.589 --> 00:08:49.198 It's going to on and E, so I could type in, um. 78 00:08:52.109 --> 00:09:00.749 Say say for 224 and say point 5 for the probability. 79 00:09:00.749 --> 00:09:09.149 You'll get something like this is the probability of selecting exactly. 22 items out of 4 when it probably barely any 1 item say. 80 00:09:09.149 --> 00:09:14.818 It is point 5 so that will be 4 choose 2, which is 6 times point. 5. 81 00:09:14.818 --> 00:09:19.408 Point 5 to the 4, let's say, um, and we could. 82 00:09:19.408 --> 00:09:24.448 We can call back previous lines if you like. So here I could put it in. 83 00:09:24.448 --> 00:09:32.729 Chilly, I'll put in a string 0 to 4 and I have to put a comma. 84 00:09:35.009 --> 00:09:39.869 And so these are the binomial probabilities. 85 00:09:39.869 --> 00:09:44.458 For any equals 4 and K going from 0 up to 4. so. 86 00:09:44.458 --> 00:09:51.418 Point 0, this is 116 or 16. 616th 46,116. so. 87 00:09:51.418 --> 00:09:55.438 We can, we can see something like that and. 88 00:09:55.438 --> 00:09:58.859 That's something bigger. 89 00:09:59.999 --> 00:10:04.469 You want to see instead of 45 you say, say, point 7 or something and. 90 00:10:04.469 --> 00:10:10.349 Whatever, and you could write functions and so on. So you can do the calculations with this. So, this is. 91 00:10:10.349 --> 00:10:16.619 By now you could compute it by hand, it's time speed is the K times queue to the. 92 00:10:16.619 --> 00:10:22.979 In minus K. okay. You could put that. That's binomial. That 1 is easy. Um. 93 00:10:22.979 --> 00:10:30.208 It does other things geometric normal. Let's do uniform uniforms. You could say. 94 00:10:30.208 --> 00:10:35.969 That's the PDF you can also get the cumulative if you wanted. 95 00:10:35.969 --> 00:10:39.599 It'd be. 96 00:10:39.599 --> 00:10:45.899 And it's added going up to 1 and so on. Let's do it for the fair thing. Not the bias thing. 97 00:10:45.899 --> 00:10:49.619 Okay, so it's up to 1, um. 98 00:10:49.619 --> 00:10:56.458 You don't just show you how the obvious thing we could do is say uniform it's going to be flat. Um. 99 00:10:56.458 --> 00:11:01.798 And I don't know what the arguments are. 100 00:11:01.798 --> 00:11:05.519 Um. 101 00:11:05.519 --> 00:11:09.688 Typing take a guess here. 102 00:11:09.688 --> 00:11:13.019 Hello. 103 00:11:15.928 --> 00:11:19.288 Hello. 104 00:11:20.578 --> 00:11:29.729 Um, discreet uniform, get what they are, but in any case, um. 105 00:11:29.729 --> 00:11:34.499 Move on to that to say normal distribution we could do. 106 00:11:38.009 --> 00:11:45.178 Whatever the arguments are, they're probably something like mean and standard deviation as a guess. 107 00:11:46.558 --> 00:11:54.208 I look at my notes here. Okay. It's a re, evaluate it at a range of values. Okay. So. 108 00:11:57.058 --> 00:12:00.359 Let me try you in a form. 109 00:12:00.359 --> 00:12:03.839 Um. 110 00:12:11.339 --> 00:12:14.879 Hello. 111 00:12:14.879 --> 00:12:20.038 Yeah oh, okay. So a uniform. 112 00:12:32.543 --> 00:12:46.943 So, the uniform just, it's a uniform distribution or the tenant, and I evaluated the numbers. So the 0, colon point 1.1, as a point to evaluate that in the next 2 arguments are the definition of the uniform. It's uniform from 0 to 10. 113 00:12:48.509 --> 00:12:53.009 And we could put in instead of PDF, we could put in. 114 00:12:53.009 --> 00:12:59.729 And so on oh, good. Okay. Getting back to the normal. 115 00:13:01.168 --> 00:13:07.168 Okay, so it wants a value to evaluate it at and then the mean and the standard deviation, I'm guessing. 116 00:13:07.168 --> 00:13:13.798 Let's try that probably about right um. 117 00:13:13.798 --> 00:13:19.109 Now, we could evaluate it at a pile of values. Um. 118 00:13:19.109 --> 00:13:26.369 Let's go from -3 to 3 and steps of 1. let's say. 119 00:13:26.369 --> 00:13:33.509 Um, -3 to 3. I had it 3 to 3. um. 120 00:13:33.509 --> 00:13:41.038 Good. That'll be That'll be the normal. The calcium I could get the. 121 00:13:41.038 --> 00:13:46.438 Okay, so. 122 00:13:46.438 --> 00:13:51.749 Point 1% chance it's less than -3. sigmas. 123 00:13:51.749 --> 00:14:00.599 Point oh, 1.12% chances less than 2 signals. 15% chance. It's less than a segment below the mean. 124 00:14:00.599 --> 00:14:07.798 50% chance is less than the mean and so on. So you can work with stuff like this. You can then plot things. 125 00:14:07.798 --> 00:14:12.418 And, um, trying to remember how to plot it, I could say. 126 00:14:12.418 --> 00:14:16.168 A close that, and I don't know. 127 00:14:16.168 --> 00:14:21.058 Don't know what will happen here. Yeah. 128 00:14:22.379 --> 00:14:27.599 So, part of the CDF, for example, um. 129 00:14:27.599 --> 00:14:34.168 I could flock to PDF. 130 00:14:36.328 --> 00:14:39.688 I can just do a direct plot actually. 131 00:14:46.109 --> 00:14:49.859 And I see, it's trying to pop up health information to help me. So. 132 00:14:49.859 --> 00:14:55.649 Plot to PDF. 133 00:14:57.448 --> 00:15:02.759 Of course. 134 00:15:02.759 --> 00:15:17.519 Where did you go? Are we going to hear famous bell curve? Let's say it's a little blocking because I'm only evaluated every 1. maybe I want to evaluate it a little more. 135 00:15:17.519 --> 00:15:22.649 A few more points instead of every 1. let me do it at every point. 1 lets say. 136 00:15:26.698 --> 00:15:30.359 And this will look a lot more like a famous bell curve. 137 00:15:32.009 --> 00:15:37.379 Okay, so you plot stuff in Matlab, computer stuff and stuff and so on. 138 00:15:38.548 --> 00:15:43.139 Again, it's a, why do you use package even though our API. 139 00:15:43.139 --> 00:15:50.578 We are not so explicit always above, requiring you to learn it. I think any engineer should become aware of. 140 00:15:50.578 --> 00:15:53.729 Aware of the Matlab. 141 00:15:55.558 --> 00:15:59.729 And. 142 00:16:01.948 --> 00:16:06.719 And again, I've got a few couple of points here. Arc. 143 00:16:06.719 --> 00:16:12.778 From our plots and so on. Oh, nice interactive thing called this tool. 144 00:16:12.778 --> 00:16:16.619 Thanks. 145 00:16:17.818 --> 00:16:25.828 Okay, so you can pick a distribution, let's say, look at the PDF here. 146 00:16:25.828 --> 00:16:31.139 Um, and then you can, um. 147 00:16:31.139 --> 00:16:45.984 Play games with it, or you can set me when Sigma, some use the means. So if we make it 1, instead of 0 whole thing shifts to the right if we make this Sigma say 2, instead of 1, it gets broader, all that sort of stuff. Instead of normal. 148 00:16:46.619 --> 00:16:50.609 You could look at Hassan or something. 149 00:16:50.609 --> 00:16:59.849 Okay, so you can look so, plus on Lambda, that's the mean we make it say. 150 00:16:59.849 --> 00:17:05.278 It could be a fraction, so it could be point 4 or something. And then. 151 00:17:05.278 --> 00:17:08.878 Oh, I better make the upper bound a little higher um. 152 00:17:08.878 --> 00:17:13.169 Lower bound say Sarah. 153 00:17:13.169 --> 00:17:16.199 Okay. 154 00:17:16.199 --> 00:17:20.969 It goes down, Greg, I may make, let him say 3 or something. 155 00:17:20.969 --> 00:17:29.038 So, with with Lambda, very small tails off, like an exponential sort of like a falando was 1, this is what we get. 156 00:17:29.038 --> 00:17:40.858 Nicole say, 2, but if we make Glam to say 20, instead of 2, it's getting to be fairly good to a Gaussian a normal. So. 157 00:17:41.909 --> 00:17:45.719 This is this thing, and even at 5, um. 158 00:17:45.719 --> 00:17:49.499 It's almost, you know, it looks pretty symmetrical, so. 159 00:17:49.499 --> 00:17:54.959 So, for lamb to say, bigger than 5 or so, Gaussian the reasonable approximation. 160 00:17:54.959 --> 00:17:59.909 Well, we may touch bigger to be safe to say 8 or something, you know, it's going to be. 161 00:17:59.909 --> 00:18:04.679 Reasonable approximation. Certainly for land equals 10 normals quite a good. 162 00:18:04.679 --> 00:18:15.148 Would look quite good for that. So, this is our, um, our, this tool in Matlab you can get a, you can look at stuff and there's other things here. I didn't talk about. Yeah so. 163 00:18:16.618 --> 00:18:23.939 Um, didn't have fun with exponential just goes down like that. 164 00:18:23.939 --> 00:18:27.449 So, and I mentioned this. 165 00:18:29.278 --> 00:18:35.009 Um, random numbers it does, for example, um. 166 00:18:35.009 --> 00:18:40.739 No, you can say. 167 00:18:40.739 --> 00:18:47.909 Can random numbers from 0 to 1 and so on to. 168 00:18:47.909 --> 00:18:55.979 Other things I mentioned here, um. 169 00:18:57.598 --> 00:19:02.999 Do interactive you call you can plot 2 things at once um. 170 00:19:04.229 --> 00:19:12.568 I mentioned that here, try this. 171 00:19:12.568 --> 00:19:17.278 So, again, let's just make a set an interval say. 172 00:19:17.278 --> 00:19:20.368 X equals say -3. 173 00:19:20.368 --> 00:19:29.999 And steps the point 1.12 steps, the 3-3 to 3 and steps the point. 1. 174 00:19:29.999 --> 00:19:33.209 And now I can do a PDF of that. 175 00:19:33.209 --> 00:19:37.078 Take normal. 176 00:19:37.078 --> 00:19:40.138 And 0 and 1. 177 00:19:41.848 --> 00:19:47.788 X, Where's our plot here? 178 00:19:50.009 --> 00:19:53.519 Wow. 179 00:19:53.519 --> 00:19:59.068 Flight X I want to plot, um. 180 00:19:59.068 --> 00:20:03.419 1, sorry. 181 00:20:03.419 --> 00:20:07.469 And that's going to be. 182 00:20:08.578 --> 00:20:13.528 Yes, okay. Um, and then what I have in my notes. 183 00:20:15.449 --> 00:20:25.348 Is I could I could do another 1 to say with the standard deviation of 2 I could say and 2 we come on. 184 00:20:25.348 --> 00:20:28.558 And 2 equals PDF. 185 00:20:28.558 --> 00:20:38.128 Normal values of X, let's say, mean 0 and Sigma 2. 186 00:20:41.338 --> 00:20:45.898 And what it's going to be and where does that plot go. 187 00:20:47.939 --> 00:20:51.898 Well, rescaled itself, so you can't tell it's really going out. 188 00:20:52.979 --> 00:20:57.148 It's not that broad. Let me kill the 2 plots. 189 00:20:58.439 --> 00:21:01.618 Let us get started again. Um. 190 00:21:03.148 --> 00:21:11.368 2, well, it didn't have a chance to tail off so much so it's sorta weird. 191 00:21:12.628 --> 00:21:18.778 Um, so what I show here is, I can plot 2 things at once so this will be X and. 192 00:21:18.778 --> 00:21:22.229 And let's try that, let's see. 193 00:21:25.078 --> 00:21:30.449 Yes, cost away. 194 00:21:30.449 --> 00:21:34.019 I'm attempting to record it on Webex. 195 00:21:34.019 --> 00:21:42.479 Um, my camera is on, so it is spying on me at the moment. And if we go to here. 196 00:21:42.479 --> 00:21:46.769 Is it recording. 197 00:21:46.769 --> 00:21:51.118 Yeah. 198 00:21:51.118 --> 00:21:54.148 It should be recording the whole screen. Yes. 199 00:21:55.288 --> 00:22:04.769 However, if you've tried to look at my recordings, a fair amount of the time, something goes wrong. The reason is that my technology, I'm just doing too many different things at once. So. 200 00:22:06.659 --> 00:22:10.528 Can check it check it right now and see, um. 201 00:22:10.528 --> 00:22:14.788 Okay. 202 00:22:14.788 --> 00:22:25.108 So, back to Matlab and math lab, if you don't like the way I talk this piles of information online about it, but in any case, so we can say. 203 00:22:25.108 --> 00:22:28.469 Say X. 204 00:22:28.469 --> 00:22:33.929 Ex comma you check it right now and see if it's actually working. 205 00:22:33.929 --> 00:22:36.929 Hello. 206 00:22:38.909 --> 00:22:48.538 Good occasionally things work. Okay so that's plotting experts in 1. I could say plot experts. 207 00:22:48.538 --> 00:22:52.288 And 2. 208 00:22:52.288 --> 00:22:59.818 Let me see, you have to say X again, maybe. 209 00:22:59.818 --> 00:23:03.088 Okay. 210 00:23:03.088 --> 00:23:07.919 The part of the 2 of them at the same time. So. 211 00:23:07.919 --> 00:23:12.058 What would be. 212 00:23:12.058 --> 00:23:15.179 I might build it into a homework. Yes. 213 00:23:15.179 --> 00:23:19.409 So, yes. 214 00:23:20.578 --> 00:23:27.269 Well, it would be specifically Matlab I would think, because I'd construct something using Matlab. So. 215 00:23:28.348 --> 00:23:32.189 Um. 216 00:23:32.189 --> 00:23:39.388 Well, tell me, what else would you be thinking of using a, a statistics package in Python or or what else are you thinking of. 217 00:23:41.068 --> 00:23:47.999 Hello. 218 00:23:47.999 --> 00:23:51.479 Computer for 1 point. 219 00:23:51.479 --> 00:23:56.159 Gone. 220 00:23:56.159 --> 00:23:59.548 Well, you can download and install it again. 221 00:23:59.548 --> 00:24:07.858 I believe you can, there's a problem, the faculty and the students at our slightly different views of Matlab. 222 00:24:07.858 --> 00:24:11.578 I actually installed this on this machine here last night. 223 00:24:11.578 --> 00:24:15.088 I don't know what the student view is. 224 00:24:15.088 --> 00:24:19.138 But, um, I think it's. 225 00:24:19.138 --> 00:24:24.778 You connect do the math works? Web site? That's a company that does the Matlab. 226 00:24:24.778 --> 00:24:27.838 And I think you install it from their website. 227 00:24:27.838 --> 00:24:33.449 But again, the view I see is not always the same as the view of the students say. 228 00:24:33.449 --> 00:24:38.608 What is trying to do is minimize licensing costs because. 229 00:24:39.838 --> 00:24:42.929 Matlab is expensive. Um. 230 00:24:42.929 --> 00:24:57.659 I like a joke into more of a sort of sense that it's, you know, these companies have the drug dealers business model. 1st, 1 is free or something. They get you addicted and. 231 00:24:57.659 --> 00:25:10.048 You're hook because something like Matlab you see and even if you think you're getting a perpetual license, every they update it and you'd have to buy a new license to get the new version as the new features. 232 00:25:10.048 --> 00:25:21.179 And once your company is committed to this, it'd be very difficult to change because there's no exact match, you know, competitive model. But if you stay with it, it is very nice. 233 00:25:21.179 --> 00:25:30.929 So, um, and then the other 1, I'll show you is some other time it's Mathematica. That'll be optional but that works with algebra. 234 00:25:32.278 --> 00:25:35.519 In any case, so you can, um. 235 00:25:36.989 --> 00:25:40.739 Go in here and plot several things at once. 236 00:25:40.739 --> 00:25:44.909 I think you can go in and. 237 00:25:44.909 --> 00:25:48.088 Does this work. 238 00:25:50.159 --> 00:25:55.199 Yeah, you see, I just boxes in and stuff like that. 239 00:25:55.199 --> 00:26:01.588 And I talk about it on on the webpage. 240 00:26:01.588 --> 00:26:08.669 Here so, gosh is dot Jason so on. 241 00:26:10.409 --> 00:26:13.528 Hello. 242 00:26:19.259 --> 00:26:24.689 What's a close quote? 243 00:26:26.429 --> 00:26:32.578 Call yeah, so. 244 00:26:32.578 --> 00:26:36.778 You know, green, something that. 245 00:26:36.778 --> 00:26:44.128 So, you can have fun with that. Okay. And again, what I'm showing you right now is a very superficial view of it. You can actually. 246 00:26:44.128 --> 00:26:49.528 Get much deeper and more complicated where he transforms and so. 247 00:26:49.528 --> 00:26:55.378 Okay, um, and have fun. 248 00:26:56.519 --> 00:27:03.298 Okay, so what are my notes on Matlab there? Like. 249 00:27:05.368 --> 00:27:14.068 And, and just my points here, this is my opinion about it. It's very powerful. 250 00:27:14.068 --> 00:27:18.898 For stuff like, say, inverting sparse makes sense for complicated, numerical stuff. 251 00:27:18.898 --> 00:27:25.828 They sometimes they hire the best people in the field, but they'll, they'll hire the best mathematicians. 252 00:27:25.828 --> 00:27:29.788 On the topic to do their algorithm so. 253 00:27:29.788 --> 00:27:41.699 You know, the state of the art stuff and, I mean, things, like I said, in solving big linear systems that are sparse over determined air conditioned or something and, um, it's got dozens of toolkits available. 254 00:27:41.699 --> 00:27:45.719 Um, show you a list of them maybe next time. 255 00:27:45.719 --> 00:27:54.989 It can exploit hardware. It will do column. If you have a g deal attached, it will do common things. The GPU parallel computers. 256 00:27:54.989 --> 00:28:00.868 Everything is a parallel computer, this little laptop here. Um, I can show you it's. 257 00:28:05.009 --> 00:28:10.108 To start another screen in here. 258 00:28:10.108 --> 00:28:13.618 So, I'm on. 259 00:28:13.618 --> 00:28:21.449 This little laptop here is a dual 4 core Intel so it's an 8 core 8, hyper thread machine. You can see there. 260 00:28:21.449 --> 00:28:28.169 A threat, so, um, and Matlab will take advantage of that. 261 00:28:28.169 --> 00:28:35.278 Um, it's interactive, you can write, you can write programs, or you can just type in small commands and they immediately. 262 00:28:35.278 --> 00:28:40.318 Execute as I just showed you and it. 263 00:28:40.318 --> 00:28:46.229 Or you can take these commands and put them in a function, which it will run. No need to have a separate compile run. 264 00:28:46.229 --> 00:28:49.558 And it's got piles of stuff, um. 265 00:28:51.328 --> 00:28:57.749 Look at this, come on so on the right we've got all of the variables that created in this session. 266 00:28:57.749 --> 00:29:07.378 Um, over here, um, and how big they are at the left, I've got various other functions that are files that are in the same directory. 267 00:29:07.378 --> 00:29:14.038 And got piles of stuff I can this is a work workspace, I can save it and resume it. 268 00:29:14.038 --> 00:29:17.038 All that sort of files and files and files of resources. 269 00:29:17.844 --> 00:29:27.263 Oh, so there's piles of stuff available. Course once you leave, it will get expensive. It's a funny programming style. 270 00:29:27.263 --> 00:29:33.624 However, you data structures you have to force them to look like a race if your data structures are link lists and trees and so on. 271 00:29:33.898 --> 00:29:40.439 It's going to be tricky to use the stuff fun stuff that they teach and data structure. It's going to be tricky to do that in math lab. 272 00:29:40.439 --> 00:29:47.848 But the trouble is the alternatives there are free clones, but they're not very good. However. 273 00:29:47.848 --> 00:29:53.009 If you like C, + + and I actually like C + plus a lot. 274 00:29:53.009 --> 00:29:58.318 C, +, plus free libraries that do a lot of what Matlab does. 275 00:29:58.318 --> 00:30:06.118 Because the mathematicians that are paid to write, provide stuff for Matt, and I may also provide C + plus versions for free. Perhaps. 276 00:30:06.118 --> 00:30:10.888 The trouble with sequel, it's using template matter programming. 277 00:30:10.888 --> 00:30:21.239 Which is and the code sort of looks like Matlab, but if you make a syntax error in your program, the compiler error messages are impossible to understand. 278 00:30:21.239 --> 00:30:27.929 But, see, let's, let's also runs fast so any case so that was, um. 279 00:30:27.929 --> 00:30:33.538 That was Matlab. Are there any questions about that? 280 00:30:34.769 --> 00:30:38.128 And again, it has excellent. Um. 281 00:30:38.128 --> 00:30:42.449 It has again state of the art. Excellent. 282 00:30:42.449 --> 00:30:45.538 Algorithms underneath it, so. 283 00:30:46.104 --> 00:31:00.804 For example, you're inverting a matrix, which is almost singular to determined is very small. It's very tricky to invert it and not lose all of the significant digits and get a divide by 0 during the inversion process. Oh, Matlab will handle that. 284 00:31:01.078 --> 00:31:05.338 Seems like that you have a very large matrix 1000 by a 1000 matrix. Let's say. 285 00:31:05.338 --> 00:31:11.638 Matlab will do that so that's the advantage of that. So. 286 00:31:12.929 --> 00:31:20.939 A competing package, I'll show you what not and whom something called mathematically. It does algebra. 287 00:31:20.939 --> 00:31:27.328 You give it an expression with variables and functions and integrate differentiate plot and do stuff like that. 288 00:31:27.328 --> 00:31:32.759 So, okay now, um. 289 00:31:32.759 --> 00:31:36.898 I was trying to do okay. 290 00:31:38.848 --> 00:31:41.909 Oh, yeah, I forgot. I'm missing a line. 291 00:31:42.114 --> 00:31:56.874 In my program here, um, I left the line out of the source code for the blog, so it's not rendering the mathematics. Right? If you're curious, this is what I actually type in the blog with my editor, and it gets rendered as mathematics. So. 292 00:31:57.179 --> 00:32:00.689 I'll get that for next time. Um. 293 00:32:03.179 --> 00:32:08.219 So, in any case, let me see if I can. 294 00:32:08.219 --> 00:32:14.459 I can just see if I, um. 295 00:32:14.459 --> 00:32:18.598 I'm trying is probably not working. 296 00:32:21.419 --> 00:32:26.009 Was working at 1 point in the past. 297 00:32:29.338 --> 00:32:33.719 Huh. 298 00:32:36.239 --> 00:32:40.378 Hello. 299 00:32:40.378 --> 00:32:44.608 I get that again. 300 00:32:54.088 --> 00:32:57.568 Huh. 301 00:33:00.538 --> 00:33:08.189 Okay. 302 00:33:09.689 --> 00:33:14.788 No, okay. Um. 303 00:33:16.169 --> 00:33:22.888 So, what I'll have to do for people, watching me remotely is I'm switching over. 304 00:33:22.888 --> 00:33:30.028 To the switching over to my iPad so I'll have to stop. 305 00:33:30.028 --> 00:33:33.479 Or the session and restart the session. 306 00:33:33.479 --> 00:33:36.689 On the iPad, because I can't mirror the iPad. 307 00:33:36.689 --> 00:33:42.058 Busy well, let me try it. 1 thing. 308 00:33:43.528 --> 00:33:47.608 Hello. 309 00:33:47.608 --> 00:33:55.108 Let me see if this actually works here. Um. 310 00:33:57.179 --> 00:34:01.469 Hello. 311 00:34:01.469 --> 00:34:04.528 Okay. 312 00:34:08.818 --> 00:34:12.509 Okay. 313 00:34:12.509 --> 00:34:18.119 Okay. 314 00:34:18.119 --> 00:34:21.838 Okay. 315 00:34:23.579 --> 00:34:28.798 I'll give us a try to see if this works. It's this. 316 00:34:28.798 --> 00:34:33.898 Um. 317 00:34:36.594 --> 00:34:48.713 The problem is that I'm in a mode now where, when I touch my stylus to the screen, where it makes a mark is not where I'm touching. It's the sort of thing that. 318 00:34:49.349 --> 00:34:58.768 Drive you a little bonkers bonkers looking at that. Um, but we'll give her a try and see what happens. 319 00:34:58.768 --> 00:35:04.079 Okay, so. 320 00:35:04.079 --> 00:35:08.398 You are. 321 00:35:10.409 --> 00:35:18.059 Okay, so what I want to do is tutorial on probability, um, density. 322 00:35:18.059 --> 00:35:21.869 This is. 323 00:35:25.228 --> 00:35:29.548 This is not gonna work. Um, let's see. 324 00:35:34.798 --> 00:35:43.889 So, help you understand that, um, suppose you've got something like. 325 00:35:43.889 --> 00:35:48.298 F, X equals say 1. 326 00:35:48.298 --> 00:35:52.768 I say live and 0 else. Okay. 327 00:35:53.849 --> 00:35:57.449 And suppose I say that. 328 00:35:57.449 --> 00:36:02.969 Hello. 329 00:36:09.929 --> 00:36:13.619 Hello. 330 00:36:13.619 --> 00:36:20.489 Those are defined, say, um. 331 00:36:20.489 --> 00:36:24.628 Well, as I say. 332 00:36:26.398 --> 00:36:31.798 Y, equals 2 x then what is f of Y. 333 00:36:33.148 --> 00:36:38.969 And to try to try to motivate this. 334 00:36:43.018 --> 00:36:48.028 Slightly different, let me say something like. 335 00:36:50.159 --> 00:36:58.409 Let's say why it goes 2.54 X. okay. So, X is something in inches. 336 00:36:58.409 --> 00:37:04.079 And why is something in centimeters? Let's say. 337 00:37:04.079 --> 00:37:07.409 So, Texas, the length of stuff. 338 00:37:07.409 --> 00:37:15.329 It's a span of 6 inches then Y, in centimeters, it would be 15 centimeters. Let's say so. 339 00:37:19.139 --> 00:37:25.018 So, if I pick a, and let's, let's use the example of the pen, and let's say. 340 00:37:25.018 --> 00:37:29.278 0, less than equal to X, less than or equal to 6, let's say. 341 00:37:29.278 --> 00:37:33.119 Which would mean 0, less nickel for wireless sake of 15. 342 00:37:33.119 --> 00:37:38.518 Okay, so if it's something that's uniform than. 343 00:37:38.518 --> 00:37:44.728 There'll be 1 over 6 for 0 less than less than equal to 6. okay. 344 00:37:44.728 --> 00:37:49.648 And clearly f, Y, we'll be won over. 345 00:37:49.648 --> 00:37:53.759 15. 346 00:37:53.759 --> 00:38:00.568 Okay, now, how, how would we count? I mean, that's just intuitive. Okay if, if everything is uniform. 347 00:38:02.699 --> 00:38:08.579 Okay, um, well, this is an aside in the United States. 348 00:38:08.579 --> 00:38:12.719 A niche for most purposes is legally. 349 00:38:12.719 --> 00:38:16.769 I said 11 point it, it's. 350 00:38:16.769 --> 00:38:20.880 1, over 2.54 centimeters. Exactly. 351 00:38:20.880 --> 00:38:27.690 So, a niche is exactly 2.54 centimeters legally in the United States for most purposes. 352 00:38:27.690 --> 00:38:31.710 Except that per surveying purposes. 353 00:38:31.710 --> 00:38:38.159 It's different after surveying purposes, legally. 354 00:38:38.159 --> 00:38:42.449 A meter is 39.37 inches. Exactly. 355 00:38:44.159 --> 00:38:49.619 Now, the problem is that those are 2 different definitions relating English in metric in the United States. 356 00:38:49.619 --> 00:38:53.699 And they differ in about 1 part and tend to the 8th. 357 00:38:55.019 --> 00:39:02.400 People don't much worry about it. I guess you just have to say what type of what type of thing it is. 358 00:39:03.539 --> 00:39:09.989 Um, because 2.54 times, 39.37 is not precisely a power and. 359 00:39:09.989 --> 00:39:20.159 Okay, so so you just intuitively if I've got a random variable, it's uniform from 0 to 6. it's a random point on on this 10. 360 00:39:20.159 --> 00:39:23.820 And then the density function is 1 6. 361 00:39:23.820 --> 00:39:28.920 In that interval and 0 website and if I. 362 00:39:30.480 --> 00:39:39.630 Consider this as centimeters instead of inches and 15 centimeters and its uniform. The density function is 115. 363 00:39:39.630 --> 00:39:44.010 Okay, um. 364 00:39:44.010 --> 00:39:48.809 Now, in this case, you're going to totally see what's going on and the way it's done. 365 00:39:48.809 --> 00:39:52.860 Using formulas is, um. 366 00:39:52.860 --> 00:39:56.639 Here. 367 00:40:00.869 --> 00:40:04.650 Okay, so so we have, um. 368 00:40:06.150 --> 00:40:12.659 So particular value to get from extra why it's why it was 2.54 what's going on. 369 00:40:12.659 --> 00:40:18.210 Y, equals. 370 00:40:19.769 --> 00:40:23.820 I have 2.54 X. 371 00:40:23.820 --> 00:40:32.670 And again, if you're wondering why my handwriting so messy, it's where I'm writing is an inch above on the screen where it's actually writing. So. 372 00:40:32.670 --> 00:40:38.039 In any case so D Y, over dxi, um. 373 00:40:39.449 --> 00:40:45.300 And I forgot what is going to be. 374 00:40:46.619 --> 00:40:51.389 It's going to be actually. 375 00:40:51.389 --> 00:40:58.619 Um, it's actually going to be the reverse it's going to be. 376 00:40:58.619 --> 00:41:02.070 By D. Y X. 377 00:41:02.070 --> 00:41:06.539 So you could, you could look at it this way off of why D, why. 378 00:41:06.539 --> 00:41:13.079 Equals X times DX you can look at it as something like that. For example. 379 00:41:13.079 --> 00:41:16.619 I got it, it's more legible. If you look on my blog. 380 00:41:16.619 --> 00:41:24.150 So you can, this is how you convert the density function from 1 variable to another variable function of it. So. 381 00:41:25.619 --> 00:41:30.809 Um, no, on Tuesday, it's similar. 382 00:41:30.809 --> 00:41:35.849 I mean, suppose I've got a target here, um. 383 00:41:37.679 --> 00:41:41.099 And so it's 1 for. 384 00:41:41.099 --> 00:41:45.630 By 1 foot and I'm picking a point. 385 00:41:45.630 --> 00:41:55.469 X Y, and then the density so it's going to be. 386 00:41:55.469 --> 00:42:00.000 Oops. 387 00:42:00.000 --> 00:42:05.190 So, if it's uniform and f, X and Y equals. 388 00:42:07.710 --> 00:42:12.360 And why. 389 00:42:12.360 --> 00:42:19.199 Equals 1, let's say 0 less than equal X less than equal 10 less than y1 to 0. otherwise. 390 00:42:20.639 --> 00:42:28.739 Okay, and then 0 else. Okay. And if we convert say, if we say convert to metric. 391 00:42:31.980 --> 00:42:36.989 That's weird here. Um. 392 00:42:41.789 --> 00:42:50.849 I thought I had a fix for the pen and the screen being misaligned. The fix wasn't working. I'll have to re, compute it. 393 00:42:50.849 --> 00:42:56.639 Okay, so. 394 00:42:56.639 --> 00:42:59.639 Convert the metric. 395 00:42:59.639 --> 00:43:07.469 Instead of X and Y, let's call it you and V or something so you equals 30 x equals. 396 00:43:07.469 --> 00:43:20.219 30, why? And then so f of U. N. V. is going to be 1 over 900 realistically you less than equal to 30 and dental with be. Okay. 397 00:43:20.219 --> 00:43:24.449 Um, and again. 398 00:43:26.070 --> 00:43:30.300 The way you're going to get the 900, is that if we. 399 00:43:31.739 --> 00:43:35.219 So, we're working actually working with Jay Colby in this time. 400 00:43:35.219 --> 00:43:42.150 And you're going to use a. 401 00:43:43.710 --> 00:43:47.280 And the 1, the 1 over night, come on. 402 00:43:47.280 --> 00:43:54.300 Going on here, that's going to be a Nicole. We had. 403 00:43:55.860 --> 00:43:59.340 And Nicole, and and it will be like, um. 404 00:44:02.670 --> 00:44:06.599 Like, do you over DX? 405 00:44:06.599 --> 00:44:11.519 Tv over DX. Do you over D why. 406 00:44:11.519 --> 00:44:15.989 Tv over D. why. 407 00:44:15.989 --> 00:44:19.590 I'm on I'm writing. 408 00:44:20.730 --> 00:44:25.230 So the is 30. 409 00:44:25.230 --> 00:44:28.500 Tv 0 0 and 30. 410 00:44:28.500 --> 00:44:33.840 That's 6,900. so 1950versusthe Columbian. 411 00:44:33.840 --> 00:44:44.969 And this, and this formula, you can use converting different coordinates when they're not something as simple as the scale in X. and Y, like, maybe you're converting from Cartesian. 412 00:44:44.969 --> 00:44:57.539 To polar coordinates, or something like that, decode the end of the conversion variables, which you get and I don't know which course and that will tell you how the probability density functions. Um. 413 00:44:57.539 --> 00:45:05.190 Convert so, and the kill the function just well use to transform variables for. 414 00:45:06.300 --> 00:45:17.309 But I think the example I'm using it helps you intuitively see why using the derivative or that's a Columbian would work. This idea would also work if the. 415 00:45:17.309 --> 00:45:20.400 Function between the variables was non linear. 416 00:45:20.400 --> 00:45:23.849 Like, a Y equals X squared or something. 417 00:45:23.849 --> 00:45:29.190 Then the density of how the density function converts depends on what the value of access. 418 00:45:29.190 --> 00:45:32.550 You would still do something like this to convert to it. So. 419 00:45:34.260 --> 00:45:39.420 And I talk about it on here and I'll, I'll, I'll. 420 00:45:39.420 --> 00:45:43.349 All compile the mathematics and so on to make it look mathematical. 421 00:45:44.969 --> 00:45:52.409 If you're wanting, so this is what I actually type in to create the pretty math it's called and it's something. 422 00:45:52.409 --> 00:46:00.960 No, because I left the formatting line out of the program and I didn't catch it. 423 00:46:00.960 --> 00:46:05.429 And you see, I'm using something I type. 424 00:46:05.429 --> 00:46:09.780 I typed the page is using a simple markup language called restructured text. 425 00:46:09.780 --> 00:46:14.610 And then I compiled them into HTML with a static CMS called Nicola. 426 00:46:14.610 --> 00:46:19.440 But I have to tell nichola that this math on the page, it doesn't automatically interpret it. 427 00:46:19.440 --> 00:46:22.860 And if I tell it, and then compile the page. 428 00:46:22.860 --> 00:46:26.610 Then you'll get the pretty math on the page. 429 00:46:28.170 --> 00:46:34.500 And so, within when I upload to my own, it's my own virtual web server. The RPI gives me. 430 00:46:34.500 --> 00:46:43.525 I upload the HTML, so there's a compile step separately. It's not like an interactive thing, building the page. 431 00:46:43.554 --> 00:46:49.824 Like you have on Google sites or whatever but the result is, it's less dependent on changes. 432 00:46:50.070 --> 00:46:56.039 In the system, so, and it's sufficient. I like stuff that runs fast. Um. 433 00:46:56.039 --> 00:47:01.860 I used to use something called built in PHP. I used to as a wiki called PM wiki. 434 00:47:01.860 --> 00:47:08.429 2 problems with that is it created the page every time a client request at the page. 435 00:47:08.429 --> 00:47:16.289 And as the page got more complex, it took more CPU time to create the page. And if a lot of people requested the page that would start loading down the server. 436 00:47:16.289 --> 00:47:27.719 The 2nd problem is that PHP had some changes because of security issues. So my old page is no longer compiled properly. No longer rendered properly interpreted not compiled. 437 00:47:27.719 --> 00:47:36.869 And the advantage of this compile process is that even if something in Nicola changes, I still have the HTML versions of the pages. So. 438 00:47:36.869 --> 00:47:40.050 Unless something changes in HTML. 439 00:47:40.050 --> 00:47:43.980 Okay, so that's the reasons it. 440 00:47:43.980 --> 00:47:52.019 You don't have to learn that, but should you want to this is the world's best mathematical type setting language so. 441 00:47:52.019 --> 00:47:55.860 Better than Microsoft. 442 00:47:55.860 --> 00:48:02.579 Well, anything else so just looks better. Okay. Any case. So, that was this. 443 00:48:02.579 --> 00:48:06.780 Okay, um. 444 00:48:06.780 --> 00:48:17.309 Call him again. Um, so what I've showed you is using Matlab to do some numerical stuff, and also tutorial on. 445 00:48:17.309 --> 00:48:21.389 Transforming variables 1 and 2 variables. Um. 446 00:48:21.389 --> 00:48:29.369 And then just to hit you with what's happening um. 447 00:48:29.369 --> 00:48:35.369 Oh, we're in 2 random variables. I typed some stuff in here and again, I forgot to render the thing. 448 00:48:35.369 --> 00:48:41.429 Um, and. 449 00:48:41.429 --> 00:48:44.820 But just to. 450 00:48:44.820 --> 00:48:48.269 Just to review what I talked about. 451 00:48:48.269 --> 00:48:54.119 You have the probability mass function for 1 variable for to discrete variables just list of the. 452 00:48:54.119 --> 00:49:02.579 The values the random values and what the probability at those points are. So, in 2 dimensions, it's the matrix, probably mass function. 453 00:49:02.579 --> 00:49:12.000 Perhaps of the variables, and you can integrate it, you can get the cumulative density function. It's just the integral below and left of a point. 454 00:49:12.000 --> 00:49:17.730 The argument for the, and and again in 2 variables as in 1 variable. 455 00:49:17.730 --> 00:49:23.340 The, um, you can have mixed, discreet, continuous things. 456 00:49:23.340 --> 00:49:30.449 And so some, for some cases, the random variables, continuous like, it's perhaps. 457 00:49:30.449 --> 00:49:38.940 Again, at the airport to pick up a car, and some of the time the car's right there. So that's a specific point. That has the probability. 458 00:49:38.940 --> 00:49:43.110 Otherwise you're going to wait an exponential amount of time. That's the continuous part. 459 00:49:43.110 --> 00:49:49.710 Oh, it's 2 variables. The interesting stuff is the relation between the 2 variables, which you just started seeing last week. 460 00:49:49.710 --> 00:49:55.079 The covariant, which is like the variance, but relate to 2 variables. Nearly relate to each other. 461 00:49:55.079 --> 00:49:58.530 And from that, we can compute the correlation coefficient. 462 00:49:58.530 --> 00:50:04.079 Which is which removes the units of X and Y. S dimension list. 463 00:50:04.079 --> 00:50:13.409 If you convert between English and metric the code, the code variants will change. The correlation will not change its -1 to 1. 464 00:50:14.519 --> 00:50:21.989 Okay, and that's a reasonable point to stop now, I think, rather than starting some new stuff so. 465 00:50:21.989 --> 00:50:27.750 I have a good break, and we will start up again on Monday and a week and a half. So, and I'll stay here. 466 00:50:27.750 --> 00:50:32.909 If there's questions, so. 467 00:50:32.909 --> 00:50:36.599 Cool. 468 00:50:36.599 --> 00:50:39.869 Okay. 469 00:50:39.869 --> 00:50:43.619 Hello. 470 00:50:44.969 --> 00:50:55.739 You can put it up here if you want. 471 00:50:55.739 --> 00:51:00.090 Right. 472 00:51:00.090 --> 00:51:05.699 This 1, I'm guessing we're just testing because when I actually plug it in, it came out. 473 00:51:05.699 --> 00:51:15.869 99% that it's going to be bad, but you probably want to go during office hours of male discussion. 474 00:51:15.869 --> 00:51:22.380 Uh, bring it back again, but my view is like. 475 00:51:22.380 --> 00:51:27.750 I plugged it into the what is it? Um. 476 00:51:27.750 --> 00:51:33.210 Curve and this game, why do you think Nelson would work here? 477 00:51:34.945 --> 00:51:47.755 Oh, wait, not the calcium though. What is the, uh, exponential? We didn't tell you exponentially. You see the thing and we didn't tell you anything about this. So this would be a case. You use 1 of your approximation things like. 478 00:51:48.389 --> 00:51:51.570 Mark or Chevy or something. 479 00:51:51.570 --> 00:51:56.340 Exponential because they gave us me an hour. 480 00:51:56.340 --> 00:52:01.619 Well, we didn't tell you, it's exponential, so I just thought it would fit. Well. 481 00:52:02.699 --> 00:52:10.230 Yeah, so then we use that financial to find the well there we said exponential. What the 1st. 1. 482 00:52:10.230 --> 00:52:14.489 I think you'd want to use some sort of. 483 00:52:14.489 --> 00:52:22.440 Some sort of approximations thing. Yeah, but the thing is, we could go to an office hour also. I. 484 00:52:22.440 --> 00:52:26.400 Then. 485 00:52:26.400 --> 00:52:34.679 This 11 dot P equal for it doesn't mean though, it's less than 4. it just means exactly for. 486 00:52:35.730 --> 00:52:40.889 Right. Yeah. Did you get that correct? 487 00:52:40.889 --> 00:52:48.150 I think it would be correct because okay. Yeah. What is it? It's a continuous right? If it's only a. 488 00:52:48.150 --> 00:52:51.960 Yeah, that will probably be precisely at 4 would be 0. 489 00:52:51.960 --> 00:53:01.289 Thank you. You're welcome. Yeah, so I sent you the email about the. 490 00:53:01.289 --> 00:53:08.010 Reopen or window, right? Yeah, I just haven't gotten around to to entry. Okay. Yeah. 491 00:53:08.010 --> 00:53:15.000 I give me right. Thank you. I did. Let me get back to you on that. So. 492 00:53:15.000 --> 00:53:28.349 Okay, so you send me an email I will say, I haven't sent it yet. I just went back log, but thank you. You're welcome. 493 00:53:28.349 --> 00:53:32.460 Okay. 494 00:53:33.840 --> 00:53:37.619 Oh, there are a couple of. 495 00:53:37.619 --> 00:53:41.190 I don't know who is a day or 2 ago. I mentioned. 496 00:53:41.190 --> 00:53:47.969 Wiki, so oh, well, I'm going to meet the in an hour. 497 00:53:47.969 --> 00:53:54.750 And I'll ask them how many people went to their office hours the last week or so. 498 00:53:54.750 --> 00:54:00.059 And will use their answer to decide how many office hours that need to hold in the future. 499 00:54:00.059 --> 00:54:05.579 So so if no, if almost, no, when it's. 500 00:54:05.579 --> 00:54:11.159 Having we'll cut back the 2 a week, but if lots of people came, we'll have more so. 501 00:54:12.630 --> 00:54:16.679 Oh, I don't know. 502 00:54:16.679 --> 00:54:20.670 Yeah, I got, uh. 503 00:54:20.670 --> 00:54:28.019 Right I can I sent you back and confirmed that they're not yeah. 504 00:54:28.019 --> 00:54:34.469 It'll be 1%, but we'll add it into the whole. Course we'll be out of 100 now. Okay. 505 00:54:34.469 --> 00:54:38.070 At the end, and we'll add a point for each extra credit. 506 00:54:38.070 --> 00:54:41.610 Yeah. 507 00:54:41.610 --> 00:54:47.130 Now, you're allowed to get more than 1 point if you find lots of errors that I make, you'll get lots of points. 508 00:54:48.840 --> 00:54:52.139 And now you're motivated, that would be ideal. 509 00:54:52.139 --> 00:54:57.900 Yeah, but you have to stay awake now you can't fall asleep. Okay. You've got to be paying attention to me to find the errors. 510 00:54:57.900 --> 00:55:03.539 They were mostly just looking through it already. 511 00:55:03.539 --> 00:55:06.659 It's got to be a serious error or 2 enough, but yeah. 512 00:55:06.659 --> 00:55:12.480 Thank you thank you. Well, you know, I want to motivate the good students like, you. 513 00:55:12.480 --> 00:55:16.079 And it also helps me to improve my presentation. So we all win. 514 00:55:16.079 --> 00:55:20.219 So, yeah. 515 00:55:26.730 --> 00:55:31.530 Oh. 516 00:55:32.940 --> 00:55:36.150 Hello. 517 00:55:40.769 --> 00:55:49.547 Okay.