WEBVTT 1 00:00:37.975 --> 00:00:39.265 Okay, 2 00:00:39.295 --> 00:00:39.744 well, 3 00:00:39.895 --> 00:00:44.965 if it does not particularly like me sharing the screen, 4 00:00:44.965 --> 00:00:45.715 I can walk, 5 00:00:47.365 --> 00:00:51.534 I can walk through what's happening on my website, 6 00:00:51.534 --> 00:00:53.365 which might be the best thing to do. 7 00:00:53.365 --> 00:01:04.314 Then I can see if it makes us any banter, it was sharing the screen earlier. 8 00:01:04.314 --> 00:01:17.215 So, I'm just not sharing it now so, some sort of load loading at different times of the day is what? I'm almost wondering that it works better at sometimes is the day, that other times of the day. 9 00:01:17.965 --> 00:01:32.245 But in any case, then, see, if I put this on descent, then. 10 00:01:37.194 --> 00:01:40.405 Try two different, two different screens here. 11 00:01:42.234 --> 00:01:44.334 You're saying the from two different position. 12 00:01:48.055 --> 00:01:48.834 Okay, 13 00:01:50.215 --> 00:01:50.575 well, 14 00:02:10.854 --> 00:02:11.245 well, 15 00:02:11.514 --> 00:02:18.534 I'll walk through what I prepared and then you can look at it on the on the website might even be the easiest to do. 16 00:02:19.104 --> 00:02:23.875 Anyone can bring up a web browser at the same time. And then you can see what I'm doing. 17 00:02:26.064 --> 00:02:33.294 Alternatively, you can see if it can share candid camera. 18 00:02:55.284 --> 00:03:09.925 Well, okay, well, we can walk through what I am. What I prepared on the website then, and then you can check it after. So, this will be in a sense, a facilitate, a facilitated learning thing. Sorry? 19 00:03:11.004 --> 00:03:20.425 And questions about the final exam. It'll be next Monday as as you preferred twenty four hours to do it. 20 00:03:20.425 --> 00:03:25.314 I'll put it online at four PM and you time that would be Eastern Daylight time, 21 00:03:25.884 --> 00:03:33.235 and you can come back and you'll have until four PM Tuesday to hand and the result, 22 00:03:33.444 --> 00:03:36.205 the particular technology I'm still playing with. 23 00:03:36.534 --> 00:03:44.004 You will need to know the connection. It might be direct on great scope, or you do it, and you cannot integrate scope. The exam will be optional. 24 00:03:44.425 --> 00:03:59.185 It will replace exam one higher the course weights or the exam will be forty percent and the homeworks sixty percent will drop the lowest homework and to help people lower all the letter 25 00:03:59.185 --> 00:04:00.985 grades by one category. 26 00:04:00.985 --> 00:04:15.895 So the syllabus said that ninety five and up with an eighty nine came up, was a minus, and so on ninety and up will be an, a, and eighty five and up and a minus. And so we'll lower all the letter grades by will eat them by one category. 27 00:04:17.245 --> 00:04:31.764 And also, you still have the right to after you see your grade to convert to a past. No credit. Yeah. You're welcome. So that That'll help you out someone and I know. 28 00:04:31.764 --> 00:04:40.644 You're having you you're having a tough. I agree. You didn't expect this to happen, but then, you know, we didn't expect this to happen either. So we're all trying to give a little. 29 00:04:41.305 --> 00:04:54.745 And so what I'm doing also, so, you know, deleting some stuff from the course, but I'm giving you an introduction to things and yes I'm releasing the exam Monday at four PM. 30 00:04:55.345 --> 00:05:08.214 And then you'll have until Tuesday at four PM. So this will accommodate people, you know, a good chunk of the class is now, perhaps twelve hours away. And so this will help you if you don't have to wake up at four a M, to do this. 31 00:05:08.214 --> 00:05:10.855 So, that said, we still have some standards. 32 00:05:11.125 --> 00:05:11.334 So, 33 00:05:11.334 --> 00:05:16.944 I'll be curious and seeing so you get the letter grade and after that, 34 00:05:16.975 --> 00:05:23.064 we have a form on website somewhere off with the link up, 35 00:05:23.425 --> 00:05:28.194 which you can elect to convert to a pass credit. 36 00:05:28.435 --> 00:05:38.995 So, I'm curious at what point people will want to convert from a letter great to a pass. So, That'll be interesting to see the second point on the I have on today. So. 37 00:05:39.720 --> 00:05:53.334 The today's blog for for class. Twenty four is totally coincidentally, I found a born loser comic related to the statistics below the GPA. 38 00:05:53.814 --> 00:06:06.954 Okay thanks. So so I don't actually know what are I don't even know if I could take it through various computer files and find out. I wouldn't want to know before I was doing these. Great. Okay. 39 00:06:06.954 --> 00:06:20.334 Any cases are born, lose their card to and related to one of my statistics paradoxes. Also I handed out a a homework nine. It's online now, and it's due in a week. 40 00:06:21.269 --> 00:06:29.545 Usual way on great scope. I want to try one more attempt to see if I can. 41 00:06:31.620 --> 00:06:38.574 Make these things I, I really would like to share the screen chilly if I could. 42 00:06:44.574 --> 00:06:51.925 Can you have letter grades before the final exam? Well, I won't have homework nine, but yeah. 43 00:06:54.144 --> 00:06:59.035 Good point. Well, you have your homework? Yeah. Let me try and see what I can do. 44 00:07:02.754 --> 00:07:10.944 Actually, let me try. Okay, let me just make a note before I forget. 45 00:07:21.055 --> 00:07:22.524 Okay, I'll I'll try. 46 00:07:24.569 --> 00:07:34.615 Okay, this is so. 47 00:07:35.370 --> 00:07:49.855 We're just gonna curiosity is anyone seeing my laptop screen at the moment? 48 00:07:52.045 --> 00:08:06.985 Because again, even my second computer doesn't always show me what you're showing. You're not necessarily. Okay. Okay. Any case. So, back to okay so homework nine. 49 00:08:08.339 --> 00:08:13.404 Starting to share content. Well, thank you. It would be nice if it. 50 00:08:14.730 --> 00:08:28.824 Caught up yeah I would I think is happening is, I'm hitting, my guess is that we're hitting a capacity problem with web at a prime time of the day. 51 00:08:29.519 --> 00:08:42.205 It sucks. But okay. What I can do at least is I updated the class blog for today and, and you can, you know, you can call that up. Also. 52 00:08:42.205 --> 00:08:49.044 If you want to computers in front of you, you could bring up a second window showing the class blog. 53 00:08:50.245 --> 00:09:03.684 Well, one thing, what I typed up today was some information on math lab for students. Now I was somewhat surprised actually, when a couple of people told me, they were not familiar with Matlab. 54 00:09:03.684 --> 00:09:17.845 So I asked around and the department, and I'm told, you actually were supposed to have been introduced to it in ten, ten and twenty ten. It's ninety one. It was a long time ago. 55 00:09:17.845 --> 00:09:31.524 I guess, in any case, if you, if you're not familiar with it, let me summarize it for you, it's a package for calculation and it works. 56 00:09:31.945 --> 00:09:46.764 It's you don't have to compile program if you type stuff and you get an answer, and it's designed to work with matrices. It's and it's designed. It has a lot of add on packages. That are very useful for engineers things to do a signal processing and control and stuff like that. 57 00:09:47.154 --> 00:09:59.184 So there's a very large number of packages for engineers. And it also, if you want to say work with large matrices or you want to invert matrices, it's fine. I can value stuff like that. 58 00:10:00.684 --> 00:10:14.784 It's algorithms are very efficient. They have hired as consultants some of the leaders in the fields. So, and I met the guy that did, for example, some of their matrix algorithms named Tim Davis. 59 00:10:15.894 --> 00:10:29.725 And, you know, so he does stated the, you know, computer code and his code is in math lab. He also makes stuff available for free actually, on things like a C plus plus packages. 60 00:10:30.294 --> 00:10:44.095 So, as these template libraries. So, if you know, C, plus plus, and you like playing with templates, you could get some of his algorithms, secret sauce functions for free, or you could use a Matlab. But Matlab is easier at the start. 61 00:10:44.904 --> 00:10:54.804 So, in any case, it works with matrices and you can also do for loops and so on but it's better to work with matrices and. 62 00:10:57.625 --> 00:11:03.174 And so you can do explore it, you can do very large projects on it research. You can also do exploration. 63 00:11:03.835 --> 00:11:04.225 So, 64 00:11:04.225 --> 00:11:05.455 what I've got here, 65 00:11:05.995 --> 00:11:07.284 and I would, 66 00:11:07.465 --> 00:11:07.764 I mean, 67 00:11:07.764 --> 00:11:11.274 I have a Matlab session in the background I would run if I could, 68 00:11:11.695 --> 00:11:16.585 but it's still just starting to share then unfortunately, 69 00:11:16.585 --> 00:11:17.424 I can't run it, 70 00:11:18.174 --> 00:11:24.355 but I have examples here and just simple things start off with random integer, 71 00:11:24.384 --> 00:11:25.705 random numbers, 72 00:11:25.945 --> 00:11:28.345 not round of normal uniforms. 73 00:11:29.034 --> 00:11:34.735 You can do a lot of that stuff. You can it's got functions to work with calcium, normal distribution. 74 00:11:35.065 --> 00:11:50.034 It has, it can handle about twenty of the most common probabilty distributions, normal uniform plus all discrete, discrete ones, like binomial and so on. 75 00:11:50.784 --> 00:11:55.794 And so you can so it's good. 76 00:11:56.424 --> 00:12:10.254 So let's go all the common stuff built in a lot of ones that have not discussed in class, but are in the book, I have an example here, or you can do a cumulative density function, or a probability density function. 77 00:12:10.465 --> 00:12:21.745 The thing was Matlab is it doesn't work with algebra Mathematica that I showed you works with algebra. You can tell Mathematica integrate X query. That will reply. A third of execute. 78 00:12:22.375 --> 00:12:25.705 Matlab is not that well, unless you have a call out to. 79 00:12:26.039 --> 00:12:34.134 Some algebra package and so so when it works with, say, a normal, you would give it a set of points. 80 00:12:34.134 --> 00:12:43.884 I have an example here I say, evaluate the normal density distribution function at one, two and three by the way the arguments for the normal thing. 81 00:12:44.154 --> 00:12:57.205 It's the X values evaluated at and the mean and the standard deviation and did look density function and it will return a factor of Y, values the same length as the factor X values. 82 00:12:58.315 --> 00:13:12.085 So you can evaluate the normal Kelsey and you can do random permutation sampling. And so on, okay, I've got one here. That's a little messed up. I'm sorry about that. 83 00:13:12.085 --> 00:13:24.144 It's, it's running it as it's filling. It is one paragraph I attempted to have it as separate lines. Show you how you can just type in a simple matrix. So. 84 00:13:24.600 --> 00:13:37.404 Two by two matrix elements one, two, three, four you can find the inverse. You can multiply. Just the star is is matrix model, application, dot star operator, sell and file. Multiplication. 85 00:13:37.615 --> 00:13:52.465 You can find you can add major seats element element. You can get special matrix. Nice. Like, an identity Matrix, they call it II you can find eigen values of a matrix, just hit the I. T. function. There's another function. I didn't list to find. I can factors. Also. 86 00:13:53.125 --> 00:14:05.004 If you apply one of your usual functions, like, sign Co signed square root to a matrix, it applies it element by element and returns a matrix of factor of Y, values. It's the same shape as the X values. 87 00:14:07.315 --> 00:14:20.544 Yes, you can PoC I have a function there. Oh, you can do a sequence since this works with numbers not with algebra you may often want to give it a sequence of X values. 88 00:14:20.544 --> 00:14:31.225 So, if you say zero call and ten, you'll get zero, one, two, three, six, seven, eight, nine, ten, you say zero, colon point, one, colon, ten, you'll get a sequence of every point, one from zero to ten. 89 00:14:31.524 --> 00:14:46.254 So this is the easy way to create a sequence of X values for whatever you want to do a plot. So you create a sequence of X values and C, Y, equals sign of X and assign function of peice checks returns the vector Y, values. 90 00:14:46.254 --> 00:14:48.835 And then you say X, Y, and you plot it. 91 00:14:49.554 --> 00:15:00.654 And then the plot function has all sorts of options to make the thing look beautiful. You can label your acts easy to put things in color, blah, blah, blah, blah, blah and but I gave X Y, is the simplest, possible way. 92 00:15:02.815 --> 00:15:10.075 That's for one very flexible and the to deploy. It can do very nice. Two D, plots shaded in perspective. They're a little more complicated. 93 00:15:12.355 --> 00:15:16.674 What you do is and I have it down on the blog. Here. 94 00:15:17.725 --> 00:15:30.835 You create a sequence of access, you create a sequence of wise, and you do something called mesh grid, which returns all the access repeated row after row and all the wise repeated column after column. 95 00:15:31.315 --> 00:15:40.345 And I show you the syntax, your function can return two variables. Not just one. So, what I have here is square bracket X Y, Square bracket, equals mesh grid. 96 00:15:40.644 --> 00:15:53.154 So returns to values X and Y, and the axis is rows at row are for all of the X values X sequences Y, is column after column of the Y, sequences. 97 00:15:53.695 --> 00:16:06.745 And so you take an element from the matrix and all went for the White Mitch. You got you got a unique X Y, value and I show you how you can take this and say fine sign plus costs and then gets easy to get a matrix of these. 98 00:16:07.014 --> 00:16:17.154 And then you can send it to the service function, which will do a color, a nice color shaded surface. Now that's for. 99 00:16:18.715 --> 00:16:26.695 So, that's how you can do color plots to variable three D, X Y, and Z. now specifically for the homework question. 100 00:16:27.835 --> 00:16:41.455 There's a page, which is very useful that I gave you, but what I'm telling you, here's a simplified version just for the normal for the calcium. There are other more complicated things, but, you know, if you're interested, you can start from what I've showed, you. 101 00:16:41.965 --> 00:16:52.014 Now, one thing defined help in Mathematica, Matt. I'm sorry I find it easier just to fire up Firefox and do a search. 102 00:16:52.014 --> 00:16:57.865 I say, Matlab, you know, Gaussian distribution or something and. 103 00:16:59.250 --> 00:17:06.355 So, you could inside Matlab used to help, but I find it easier just to go and search in there. 104 00:17:07.224 --> 00:17:17.575 And in any case, if you do that search, and this is a, they have a function for multi, you could search multivariate normal. I think that's probably what I did, her melted buried calcium. 105 00:17:18.144 --> 00:17:28.375 So it has a function to work with a multivariate calcium. Finally you can now see my screen. I did nothing. 106 00:17:28.375 --> 00:17:42.684 It's just the WebEx is overloaded, I think is a real Venice using Blackboards and chalk. Okay. We are now twenty five minutes into the class. You can see my screen. Okay. 107 00:17:45.414 --> 00:17:56.275 What I will do is bring up and all I can think is it's loaded. I didn't do anything at the point the screen suddenly appeared. Okay now I just have. 108 00:17:57.390 --> 00:18:10.075 The fact that people are switching off so if I turned off enough people, the survivors can see the screen, got it a few more people would. 109 00:18:10.315 --> 00:18:16.884 Okay this is totally insane but if I can somehow. 110 00:18:18.625 --> 00:18:27.924 Call up, so so I was trying to fire up Matt lab, but again I'm firing it up. 111 00:18:28.704 --> 00:18:37.914 I want to run it on a server in my lab and so I'm running s. H. 112 00:18:37.914 --> 00:18:46.734 and it's a remote accession and no, one can really get another thing. 113 00:18:46.734 --> 00:18:54.565 I don't know for, because I'm running a faculty version of Matlab, and the faculty version has actually more features than the student version. 114 00:18:54.865 --> 00:19:04.734 So I'm showing you, I can run and this be Matt lab. Okay. It's very small text. I can't help it. 115 00:19:05.424 --> 00:19:16.799 So, you can just type in stuff one plus to okay, I can create a matrix call it a cause. It's a synthesis in one place to place. 116 00:19:17.424 --> 00:19:23.275 There is a two by two matrix just out of curiosity here. 117 00:19:27.714 --> 00:19:39.265 Seventeen people left. Okay. So this, which is so the fifteen of you that are still here welcome. Thanks to the others for leaving. So you can see something. Okay. 118 00:19:39.265 --> 00:19:52.105 So, there's a two by two Matrix, if you can read the small type, and I can do the inverse of it. For example, I get that a times in verse of a, and so on okay. 119 00:19:52.105 --> 00:20:00.295 As I said is, I can't really use zoom in on this. Unfortunately, okay. If I want to plot, I mean, make a sequence of axis. 120 00:20:00.599 --> 00:20:13.470 I make it say one to ten and then I'll make Y, equals sign backs and onto a plot X. 121 00:20:13.464 --> 00:20:18.535 Y, and the plot will pop up in a separate pay screen. 122 00:20:20.634 --> 00:20:32.335 Okay, it's sorted chunky because the arguments for signer radiance, I guess so. Okay that would apply and then you could go in and edit the thing and play games with it and so on. 123 00:20:34.045 --> 00:20:48.805 Okay, so that's okay now I was gonna show you more stuff so I'm sort of caught up with let me actually pop up. Oh, I gotta show you the Cognical. 124 00:20:48.805 --> 00:20:51.295 So I took the time to link it in. 125 00:20:52.285 --> 00:20:52.944 And, 126 00:21:00.355 --> 00:21:01.134 okay, 127 00:21:01.734 --> 00:21:02.035 remember, 128 00:21:02.035 --> 00:21:04.494 I told you the statistical paradox, 129 00:21:04.795 --> 00:21:07.855 or somebody could move from a poor region to a. 130 00:21:09.444 --> 00:21:19.194 To a rich region and improve the average income of faults while here the born loser moves from one copy to another and raises the IQ at both. Okay. 131 00:21:20.545 --> 00:21:26.875 Same principle, the mathematics is the same. Okay in any case back to what you're paying for. 132 00:21:29.515 --> 00:21:33.625 I don't know, maybe you're paying for comics. I don't know any case. Did you to do? 133 00:21:35.305 --> 00:21:48.085 We can do normals and randoms and so on I mean, things like the normal CDF, whatever, whereas my Matt window my other map window. Okay. 134 00:21:50.994 --> 00:21:58.914 So, I can do something like, let me do a different set of Axis here. X equals, say, minus three to three. 135 00:21:59.755 --> 00:22:12.565 Then I can say, norm PDF say it defaults to zero in signal one. And that's and I could pod it at chilling. 136 00:22:12.565 --> 00:22:24.144 I mean, you say, why don't we get a few more points? So the thing actually looks semi reasonable. I'm gonna make in minus three and steps of point two to three. Okay. 137 00:22:24.144 --> 00:22:32.394 Why equals norm PDF X? And I do a clock X. Y. 138 00:22:34.105 --> 00:22:47.910 It will reuse a previous plot window, which will be there and very nice off to the side here. Good. You see if I want to CDF, I could say, why I see say cause norm CDF. 139 00:22:48.954 --> 00:22:49.525 Y. 140 00:22:54.025 --> 00:22:57.234 In this norm and then clock. 141 00:23:00.474 --> 00:23:13.224 And there's the over here, we have to see, okay good. Now specifically for this is one variable. And now what we can also do it for two variables. 142 00:23:14.575 --> 00:23:24.085 I'm going to what I'm going to do right now. It's actually answer the problem for you. So the fifteen of you that are still here, you get an answer to see how to do that problem. 143 00:23:24.595 --> 00:23:35.785 So the two variable normal thing it takes a vector of means, which will default to zero, but I'm gonna write it in for zero and thereby means it takes a variance matrix. 144 00:23:35.785 --> 00:23:48.055 So, the variance Matrix, now you can get the cold variance entries from the, the standard deviations and the correlation coefficient. 145 00:23:48.115 --> 00:24:00.954 So so the cool variance Matrix, which I calculated from the stuff given is going to be one because the Sigma for the first variable is the signal for the first variable was one. 146 00:24:01.224 --> 00:24:15.805 So the first entered the coherence matrix is one this here what? The second entries one point six and that is the, the second signal is to me. One point six. Okay. So what did I do here? 147 00:24:16.464 --> 00:24:17.184 I can't tell. 148 00:24:22.075 --> 00:24:24.295 Period there. Cool. Okay. 149 00:24:24.295 --> 00:24:27.954 So the one one entry is the variance of the first variable, 150 00:24:27.954 --> 00:24:28.704 which is one to two, 151 00:24:28.704 --> 00:24:30.775 two entry is different to the second variable, 152 00:24:30.775 --> 00:24:31.494 which is four, 153 00:24:31.674 --> 00:24:33.894 because it segments to now, 154 00:24:33.924 --> 00:24:34.315 the, 155 00:24:34.585 --> 00:24:34.795 the, 156 00:24:34.944 --> 00:24:37.825 the off diagonal entries are the CO variants entries, 157 00:24:38.154 --> 00:24:45.835 which are the correlation coefficient times to two segments and Sigma one times two and the row is point eight. 158 00:24:46.075 --> 00:24:59.845 So you get one point six there in there. Okay. Excuse me. So, that does the that's the variance matrix. Now. What I can do, and I got to typed in down here. 159 00:25:02.724 --> 00:25:17.605 I, I've got a list of access and what we have to do is turn it into an array of access and an array, a matrix of actions, and a matrix of wise. So I can do I can just do mesh grid. Here. I've got the access. 160 00:25:17.605 --> 00:25:24.684 I'll just use that, so I can say XM se com while I am. 161 00:25:26.394 --> 00:25:27.654 Equal smash grid. 162 00:25:33.144 --> 00:25:38.484 Guest XX good, great. 163 00:25:38.994 --> 00:25:52.704 The reason for some of this mess with stuff like mesh great is that the math lab concept of using matrices is starting to break down a little so do a mesh grid there. And then what I do is, I. 164 00:25:53.904 --> 00:26:00.894 I have my list of and I gotta make a list of pairs. So P a call say. 165 00:26:05.575 --> 00:26:12.204 Xm, this means Colin, stirring it out while I am string it up. 166 00:26:12.535 --> 00:26:24.474 Now I have a list of pairs of axes and wise and if I follow along here, because I can't remember it myself, Pete, it into mvm PDF multivariate, normal distribution PDF. 167 00:26:25.259 --> 00:26:30.474 So why goes M. G, in PDF. 168 00:26:31.944 --> 00:26:43.525 The pairs and the new variable, which I just called, em, and the CO variance matrix. Do you see the right window here? Shows things? Good. 169 00:26:43.525 --> 00:26:51.954 I got a list of wise and I have to reshape Y into a be. The same shape is the axis actually. 170 00:26:53.880 --> 00:27:01.375 What does XM so, do you want I'm sending you saying why are for reshape equals re, shape? 171 00:27:02.549 --> 00:27:06.474 Why you want to make the thirty one by thirty one Matrix? 172 00:27:07.464 --> 00:27:10.375 And then I do a surface. 173 00:27:15.265 --> 00:27:16.255 Xm, 174 00:27:16.349 --> 00:27:17.009 why, 175 00:27:17.994 --> 00:27:31.134 why are they who are it's my plot window there and right here is this thing here and here is your answer to that question. 176 00:27:33.535 --> 00:27:41.065 Now, it's interactive if okay, I can go in and I can drag it and we're okay. 177 00:27:43.799 --> 00:27:57.295 I could drag it over. Okay to hide any actual interactivity over this Internet thing. Oh, okay. Yeah, I can do that. And it's in the middle of updating now. So if surface that's looking straight down. 178 00:27:57.720 --> 00:28:10.345 So we have a surface with a counter plug underneath it. And if I had a little more interactivity, I could actually have fun with this, in any case. So, that is an example of using abusing that. 179 00:28:11.365 --> 00:28:23.994 Here's some other stuff I showed you, although the help, here's the link to the help page here and just have to reformat showing some of this stuff. 180 00:28:24.444 --> 00:28:30.204 So so that is some of the. 181 00:28:32.394 --> 00:28:44.934 You know, so that's a a quick introduction to math lab and just a second here. Okay. 182 00:28:46.434 --> 00:28:59.515 Oh, I just, I wasn't reading the chat thing. So thanks. So DJ. Yeah, so those estimated security issues so is nice to pick web safety has the infrastructure to handle all the people? 183 00:28:59.545 --> 00:29:11.305 Yeah, the well, you know, if there was better technology, I would use it, but what we're also learning, because this is the sort of thing I cannot actually test before the start of the class. 184 00:29:11.605 --> 00:29:25.494 Because, you know, it works before the class and you guys join and then it stops working. So it's even impossible for me to debug the thing without finding a hundred volunteers to sign on. Okay. In any case. 185 00:29:25.494 --> 00:29:29.664 So, that was my quick tutorial on Matt lab. 186 00:29:30.055 --> 00:29:43.134 Any Matlab questions very large package and I just gave you a quick hint to it and it says, 187 00:29:43.134 --> 00:29:50.724 I said it has a lot of toolboxes and that handle a lot of specialized things, 188 00:29:50.724 --> 00:29:51.174 not all of, 189 00:29:51.174 --> 00:29:52.615 which are licensed, 190 00:29:52.644 --> 00:29:57.805 but it is very it is very nice in that respect so. 191 00:29:59.964 --> 00:30:09.265 And as an students, you can have fun with that. Okay real productivity enhancer. 192 00:30:10.315 --> 00:30:22.555 The only downside with that is this because I've used live for quite a few years. Is this forcing everything to look like a matrix starts getting tired? 193 00:30:22.555 --> 00:30:26.005 Eventually if you more complicated data structures. 194 00:30:26.694 --> 00:30:27.954 It can be really, 195 00:30:28.224 --> 00:30:30.835 we're already seeing this a little with the surface thing, 196 00:30:33.055 --> 00:30:42.444 but it can get really hard to force complicated data structures to look like matrices and it results in what is called. 197 00:30:42.444 --> 00:30:54.924 Right? Only code it really compact code. You can do stuff in a few lines of code, but actually write the code. You kind of figure out what you yourself did because it's just forcing things to look like matrices. 198 00:30:55.134 --> 00:30:59.575 So that's an issue when you can write explicit loose but they're incredibly slow. 199 00:30:59.964 --> 00:31:13.644 But, you know, if you so, if you can make your data, look like a matrix, you're home free, because it has so many packages can handle really large matrices gigabytes. You can do stuff in parallel. 200 00:31:13.825 --> 00:31:18.025 Like, you're on a, if you're on a multi core computer, then you can do stuff. 201 00:31:18.805 --> 00:31:30.865 In parallel, if you have GPU attached, it computes things stuff like, say, inverting a matrix is compute bound. It takes time. That's the queue. 202 00:31:30.865 --> 00:31:38.125 But the number of rows of the matrix major, because number of elements is quadratic the time to process it goes up more. 203 00:31:38.394 --> 00:31:53.394 So, I can do all that in, does it all very well the problem and you can also call out to C plus plus code and stuff like that could code on and so on the problem. 204 00:31:54.295 --> 00:31:54.595 Okay. 205 00:31:54.595 --> 00:31:55.674 Like I said apart from what, 206 00:31:55.674 --> 00:31:57.535 if your data doesn't look like a matrix, 207 00:31:57.775 --> 00:31:58.734 I suppose you got all of it, 208 00:31:58.825 --> 00:31:59.694 you've got trees, 209 00:31:59.845 --> 00:32:04.555 you got trees and graphs and pointers all the good stuff you have in the data structures, 210 00:32:04.555 --> 00:32:06.894 cause that's gonna be hard to do in Matlab, 211 00:32:07.200 --> 00:32:10.375 the second point is when you add, 212 00:32:10.914 --> 00:32:18.865 it's included as part of your intuition and I didn't know what paying grant annual license fee got fifty thousand box. 213 00:32:18.865 --> 00:32:29.214 I, that's a crazy guess. But, of course, once you leave RPI and you get a nice paying job and I see the average starting K is what eighty, ninety thousand. 214 00:32:30.924 --> 00:32:45.654 And now your company has to pay a lot more to license Matlab. So I'd like to that. It's the cocaine dealers or the crack dealers model. The first one is free, but then you pay. So, not that I would know I didn't get the idea. Okay. 215 00:32:45.805 --> 00:32:58.825 So those are the pluses and minuses of Matlab. What I've personally done is graduated from Matlab writing stuff and C. plus plus I have access to the same algorithms and I've written C. 216 00:32:58.825 --> 00:33:01.555 plus plus for so many decades to match the good at it. 217 00:33:01.555 --> 00:33:03.535 So and another thing with Matt, 218 00:33:03.535 --> 00:33:05.184 that if you can write functions, 219 00:33:05.605 --> 00:33:07.075 I just haven't showed you how here, 220 00:33:07.345 --> 00:33:10.075 but once you start writing functions, 221 00:33:10.404 --> 00:33:13.164 the advantage of being interactive online system, 222 00:33:15.000 --> 00:33:18.565 that doesn't a concept doesn't scale up is the problem for large things. 223 00:33:18.565 --> 00:33:32.634 You got to be planning and designing and writing functions in advance and then you load the this is the same criticism by the way for Python. It's nice to start to do interactive stuff, but if the concept doesn't scale up to large systems, so easily. 224 00:33:33.325 --> 00:33:42.055 Okay. In case, that was Matlab I'd like to switch tracks a little for a few minutes and do statistics. One question. 225 00:33:42.055 --> 00:33:56.065 I would like to ask is many students have statistics courses in high school and other things, but many people do not and I would like to touch of feedback perhaps on. 226 00:33:57.029 --> 00:34:00.924 You know, who has had say statistics. 227 00:34:03.295 --> 00:34:10.255 Or Styx whatever you wanna call it statistics. 228 00:34:13.735 --> 00:34:27.505 In high school homework nine does not create a republic for you. Okay. Did not. Okay. Okay. Oh, good. So, this is new part of the. 229 00:34:27.505 --> 00:34:40.014 Course again you know, I, I can ask for a show of hands. I don't dare try the polling thing. And web C. T, it'll probably explode even my luck with it. Okay. 230 00:34:40.434 --> 00:34:53.755 So I have two more two more YouTube things, and what I'll do is, you can watch them on your own you'll see a better call AP statistics. Okay, great. 231 00:34:53.965 --> 00:35:07.525 You had it available, but didn't take it. No. Okay. So, what I'll do is I'll let you go asynchronous, but I have two more things in crash course statistics and just for those. That haven't had a let me first. 232 00:35:07.525 --> 00:35:17.454 What regression is that's like, when you want to compute the relation between two between two variables. 233 00:35:19.704 --> 00:35:26.275 I don't oh, well, Here's a topical one. Many people feel that the virus. 234 00:35:28.764 --> 00:35:32.275 It does not survive as well and warm weather. 235 00:35:32.969 --> 00:35:37.105 So you have some data on the web for different countries, 236 00:35:37.105 --> 00:35:39.775 say what the death rate is you might, 237 00:35:39.775 --> 00:35:43.465 and then you could look up the country's average temperature these last two months discipline, 238 00:35:43.494 --> 00:35:49.554 weather statistics and you might want to see is there a relation to warmer countries? 239 00:35:51.144 --> 00:36:04.014 Have less virus, fewer virus Des I'm going with this instead of reported cases because reported cases is such a, it depends on the testing you're doing. Okay. So that's called regression. 240 00:36:04.405 --> 00:36:18.355 And the easy thing is it was a linear regression. So the draw straight line between so X value is, say, average temperature of a country, why value is death rate? 241 00:36:18.505 --> 00:36:29.695 Not total number of deaths death rate now and you plot them it'll be a scatter plot and you try to find a relation and that's called regression. 242 00:36:29.994 --> 00:36:42.925 Linear regression now you'll get a number you'll get out of this thing is you'll get a correlation coefficient out, which will say how much of the variance of the death rate. 243 00:36:43.380 --> 00:36:51.684 Is related to temperature and it will always be less than one hundred percent and usually it's surprisingly small. So you'll get a slope for the line. 244 00:36:51.684 --> 00:36:58.764 And you'll and you'll get a correlation coefficient out, which is how much is explained now and the regression video. 245 00:36:58.764 --> 00:37:09.025 We'll talk about that and, of course, now we get into non math things, which is for men. 246 00:37:09.025 --> 00:37:21.954 If you heard, the correlation is not causation just because there is a relation just because if you do a scatterplot between temperature and death rate, you seem to see it will be aligned slowing down high temperatures. 247 00:37:22.795 --> 00:37:37.525 That doesn't mean that the high temperature caused the lower death rate, like, you know, very hot. Some of the hot countries like Africa and so they may not have had as many people travel there from infectious countries. 248 00:37:37.920 --> 00:37:39.355 Maybe maybe not. I don't know. 249 00:37:39.594 --> 00:37:39.775 So, 250 00:37:39.775 --> 00:37:41.454 that's one limitation with that, 251 00:37:41.784 --> 00:37:43.525 and another limitations are, 252 00:37:43.525 --> 00:37:45.534 if there's a non linear relation, 253 00:37:47.815 --> 00:37:49.284 many examples of that, 254 00:37:49.315 --> 00:37:50.789 in medicine, 255 00:37:50.784 --> 00:37:53.664 you get a linear relation between, 256 00:37:54.775 --> 00:37:55.344 I don't know, 257 00:37:55.344 --> 00:37:57.985 look look at the relation to water in your house. 258 00:37:58.704 --> 00:38:07.974 If you got to the water, you dive thirst if you got a medium amount of water, you're happy and healthy. If you get a lot of water, you draw. 259 00:38:08.610 --> 00:38:22.735 So, if you look at same amount of water, you have death rate. It's a U shaped curve. Okay. No water you dead. Well, so too much water. Your dad middle. You're happy. So you get these non linear relations, which are not captured. So, I'm giving you limits. 260 00:38:22.735 --> 00:38:24.445 But regression is. 261 00:38:26.275 --> 00:38:35.244 You know, it's a particular topic, and it goes onto things like multi regression where you got a lot of possible causes that are called independent variables and. 262 00:38:36.684 --> 00:38:47.125 Then you, then you try to find the variable, which has the highest correlation with the dependent variable. That's the why and then you room. 263 00:38:47.125 --> 00:39:01.164 So you'll essentially compute a new, why, where you remove the effect of the first one, then you find the second most important, independent variable and so on so you're trying to find causes. Well, it's a real thing. My roommate and I were trying in grad school. 264 00:39:01.164 --> 00:39:15.085 At one point we were looking at animal performance statistics, and the animals with red race horses at in Boston. And so we'd independent variables. How many races the horse won what does the horses average speed? 265 00:39:15.085 --> 00:39:26.155 How many dollars has it one, which is different for number races because some races pay more than and the dependent variable is is kinda like you to when it's an X Ray. So we've tried to find the most important statistic and so on. 266 00:39:27.625 --> 00:39:40.014 Well, actually, I was in it for the math thing wasn't just looking at the horses. My roommate got into the horses, and he actually dropped out of a pH. D program at Harvard infant psych. 267 00:39:40.405 --> 00:39:53.695 And then he went to law school in Canada and became a securities lawyer, so his love of racing caused him to drop out of his pH. D. program. On the other hand you got a much higher paying job. 268 00:39:54.264 --> 00:39:57.054 So any case that's regression. 269 00:39:57.355 --> 00:40:10.824 My other thing, they're non parametric statistics parametric, statistic, parameters, things like mean and standard deviation and so on non paramedic statistics are harder to explain their involving ordering and you can. 270 00:40:12.445 --> 00:40:22.375 If you can browse site and you can, if you're interested, you can look into more of that and then you can tie to current events. We're just seeing argument swell. 271 00:40:22.405 --> 00:40:35.125 You can, you can read the news you can see all these arguments about, does X affect the virus and why and so on and so on and so on one of the current fights is malarial drug help. 272 00:40:35.125 --> 00:40:47.244 So you can imagine using statistics to analyze. That does a real job dry Larry drug drive you. Crazy. Yeah, it does. Everyone knows that, but you can expect that the effect of that. 273 00:40:50.364 --> 00:41:04.614 Taking that malarial drug years ago before going to tropical places, and I don't think it drove me crazy, but, you know, you'll have to answer that one. So, in any case. So, you can look at statistics and I keep mentioning since I started the course never knew this all. 274 00:41:04.614 --> 00:41:13.344 This stuff was gonna happen about type one type two errors. You get in statistics, you have a possible drug, does it help? Does it hurt? 275 00:41:13.375 --> 00:41:21.804 Does it do nothing and just to remind you the reason for the bureaucracy, in this case, is sometimes a new drug might make things worse. 276 00:41:21.804 --> 00:41:35.335 There was that morning sickness drug for women called that caused the woman's baby when born to have no hands and feet. The baby looked like a seal had slippers not hands and feet was horrible. 277 00:41:35.755 --> 00:41:50.425 And everywhere else in the world legalized the drug and had thousands. Literally, thousands of children like this us did not have this problem because the US didn't legalize the drug. So that's statistics. 278 00:41:50.454 --> 00:41:58.255 And again, our is trying to workload this into the course a touch more of this Thursday. And then again, Monday. 279 00:42:00.085 --> 00:42:14.335 Have an exam, so I'll leave I have the chat window open that. Actually, it's to my side. I look over it to it occasionally. And I'll stay around for a few minutes in case. There's questions other than that have a good week. 280 00:42:14.335 --> 00:42:25.824 I look outside my window. It's not snowing today. It's actually warm so I see you. This will be Thursday yesterday's. So.