A lot of the understanding of statistics really began in actuary science or trying to figure out how to run insurance and make money. In fact, a lot of mathematics comes out of how to make money. So I threw in a few slides about that. I thought this was interesting because talking about the witnesses to the JFK assassination were bad insurance risks because they all ended up dead. This is a guy known for Gonzo journalism from local Kentucky named Hunter Thompson was over the top. And he wrote a pretty free style. That was one of his commentaries. He wrote about gambling. He lived on the edge and asked questions about risk. And risk is a big part of what drives study of statistics and probability. Risk assessment and risk tolerance or risk aversion. True gambling in my opinion is when there's no real assessment of risk. I thought this was a nice little anonymous poem. There was a movie called the man who never was from years ago that sort of fit it. And talking about taking risks. There was a saying that's been attributed to a lot of people but was pinned down to Frank Scully. I thought go out on the limb the fruit's out at the end. So take some chances or you don't get anywhere. And I found a point about Percules and his servant like his playing a dice. Percules for all his strength could easily lose a throw at the dice. Because fortune doesn't necessarily reflect any one thing even strength. And there's a lot of someone's yawning already. Legend about gambling and like the dead man's hand aces and eights that were dealt while Bill Hickock before he was shot in the back. And there's a lot of criminality associated with gambling. Some people that go into that often have a sketchy quality. You might not believe that. I found this it was kind of interesting kind of going into my regular time here. I need to hurry but I thought cool sign only in Texas liquor gambling smokes and God in one location. So this was just a collage and now I'm going to launch. This is what I wanted to cover in this talk and I'll let you read it. But I really want to emphasize a few points. I want to help you think about risk versus security. Certainty versus uncertainty and how you can deal with that. How you can take limited information and come to a pretty good conclusion about where the center of all that is what the thing you're looking for really is. Binomial theorem is a really, really big part of mathematics. And cobinatorics of course. And I'm going to talk about that. And binomial theorem leads to the normal distribution. I want you to end up associating the two. The normal distribution is born out of the binomial distribution. Also want to emphasize the idea of expectation. Now that was kind of confusing and used intuitively for a long time. But expectation is a generalized mathematical concept. And what we would call the first moment expectation is the mean of a distribution. And then got a couple of cool theorems by Russians leading to an easy proof of Jacob Bernoulli's law of large numbers. The wheat version is what I'm going to talk about. And I'm going to talk a little bit about Gaussian distributions. Statistics I think is interestingly duplicitous or two-faced or stands on two legs or any way you want to look at it. I think that the Roman god Janus represents it pretty well. You have the old face looking into the past and the young face looking into the future. And I think of the old face looking into the past to serve statistics and the young face looking into the future is the probability of potential opportunities. Also the other aspect of probability statistics is that it combines computational mathematics and theoretical mathematics in a way that's found really nowhere else in mathematics that I can think of. So just a quick listing of some definitions that you can look at and what statistics is. One of the important aspects of statistics and you take statistical samples and try to figure out what's going on with a larger population. You try to take them randomly. Or stochastic sampling and it's economical. It's the idea that's to save money. You can't study the entire population of anything unless it's very limited with efficiency. So by taking a sample and having tools to analyze it, you do it efficiently and effectively without using all your resources. That's how you can learn about a large universe with just a grain of sand. This little quote at the end by Stalin I wanted to counter by showing a picture of Komolkov who was an outstanding mathematician of the 20th century. He put statistics on a rigorous basis. Really brilliant guy based in Moscow. Most of his career I think. So we talk about populations and populations. We're talking about something that is out there. We're just taking little bits of it.  You have some defined procedure. One of the aspects of statistics that came out around 1950 and on from Fischer whose name you might have heard was a defined algorithmic approach to experimentation. And any more with interdisciplinary approaches to experiments. Statisticians are a good thing to have on board. So I mentioned you want to have economical thoughts about this. You usually might have grants or a certain budget you have to follow. So you have to have samples that are subsets of manageable sizes. I want to talk real quickly about some numbers. One is Pi. Where does Pi come from? Well you have similar geometric figures. You have S1 is a small arc and S2 is a larger arc centered at the crossing of these two lines. And you can create a proportionality. Well the same proportionality really will work for the entire circle. The entire circle is the full arc all the way around 360 degrees or whatever. And so the circumference of the circle to the radius is a constant. And that constant is what we call Pi. Now let me see here. Let's see. I'll just say you can estimate Pi. You can take chords which are if you look at the arc between for that C1 it's a short little arc. And the chord between the two points where the radii hit the arc make a short line segment which is very close in size to the arc. The smaller the arc the more similar it is in size to the chord. So if you subdivide a circle into n segments like this then you can figure the length of the chords. There's an easy way to do that you know. You have side angle side determines a triangle and the squares of the radii two times the radius squared times the cosine of the angle between them is equal to the chord. You can actually do computational methods to estimate Pi. That's another thing I want to encourage people to do in this but before I talk about that I want to encourage people of any age get a compass get a straight edge and see what you can do. Our comedies was at least 76 when he was slaughtered by Romans and he was drawing figures in the sand. It's not just for kids and you kind of learn things by doing this. If you take a circle there's one thing I think is really curious is that you have this area of a circle has a constant as well that same constant is used for the circumference of the circle. How did this happen? On the surface of it that doesn't necessarily have to happen but if you take a circle like I had on this table top and cut sectors bisect them and align them in opposite ways you can create a finer and finer subdivision that becomes more squared or rectangular and if you look at the lower right there each side is the length of the radius and the little arcs on each end total half the circumference so that if well by one side being related to this conference you can see that Pi would be related to the area of the circle that's being geometrically squared when you take that to a limit. You'll be cutting molecules eventually with your scissors but Kepler was the first as far as I understand who did that. There's a famous problem I want to talk about that leads into some of this and this was Bernoulli's problem of compound interest just to review this real quickly if you have whatever your interest is that you're making on an investment you add it to one and multiply it times your basis and you'll get however much the amount is going to be or grow to by whatever the interest period is. If you invest your money wisely put one euro in a bank and get 3% interest all you have to do is wait until June 13th of the 23rd year if you put it in on January 1st and your euro will become two euros so what are you going to do with all that money? In any case this equation here of one plus the interest to the nth power is what we're interested in. Bernoulli asked if you have for whatever period the principal double what happens if you compounded a half period or a fourth period and you can come up with the question what happens if you did that an infinite number times you start to look at the limit of one plus one over n to the nth power and if you go to Google and you type graph and you don't have to type four but it will state what the graph is at the top you type in the search line graph and the equation you don't have to write y or anything but some equation of x and it wants to have it in the terms of x it will give you a graph now for this particular equation it's sort of problematic as you look at the lower right hand corner there it kind of fluctuates over the place but if you you can crunch with your numbers in Google and have it calculate for 10,000 or a million or whatever and it will give you numbers closer and closer to this long number which I think isn't so hard to remember 2.7, 1828, 1828 and 45, 90, 45, 23 kind of 45, 90 is one it's double the other and then back to 45 and 23 is about half 45 so I find it easy to remember from that point and that's as far as I want to bother you might want to internalize this this numbers is important in mathematics is pi and you know someone mentioned I have difficulty with the name of the mathematician in India who wrote about pi and he estimated pi as a square root of 10 somebody popped in my head one day this e is approximated pretty nicely within one percent or so by the square root the cube root of 20 that's kind of a fun fact if you're on a desert island or looking sitting in a prison cell or something any rate there's a way of doing this when you use the power of your laptop for number crunching or graphing if you change this around this limit doesn't care if n is going toward infinity or zero it cares if that argument of one over n or n is getting larger or smaller so you can switch this around and substitute one over x for n and you get this you can take the limit of one plus x to the one x exponent and if you graph that it's a little easier you change the limit it goes toward as it goes toward zero and looking at the graph now this is a this is computational mathematics this is not you know which everything just about comes down to in some way but it's a little different in a way of expressing or discovering what e is about but if you look at it there where it crosses the y-axis at x equals zero of course one over zero doesn't exist but the limit does and that's e the number e named for oiler now I don't want to I I figured this is largely a group of people that involved in education and teaching and for mathematics much of what people learn is taught to them by maybe non-mathematicians scientists people with mathematical skills but originally I learned a significant part of statistics from a chemistry professor that's not where you want to stop but and if you do that you often will end up with bits and pieces and need to work at putting putting it together but anyway I wanted to write this out for a couple reasons I wanted to let you look at it just these are really critical concepts the being fluent or comfortable with exponents and logarithms in the mathematics of involving statistics is is critical and I want to point out the cool thing about these kinds of equations if you're dealing with functions you're trying to do some kind of functional analysis and you're dealing with functions that are multiplied together and you want to separate out those variables you may be a one function of x and another for y and x and y are independent if you take the logarithm or a logarithm of the multiple it becomes the sum of the logarithms and you can do an inverse transform back to and take the exponential function of that get it back into it's a something like its original form if you need to so it converts multiplication to addition and that helps you pry apart problems once you identify what you're trying to figure out about a system and set up a problem or model to create a an equation to derive you can often use this to derive it I wanted also to talk a little bit about the exponent or the exponential function and its derivative if you look at this the important thing I want to emphasize here is that the exponential function of whatever base is always equal to itself times a limit and that limits kind of curious interesting let's look a little further you can use graphing functions to estimate limits on this sort of thing as well and in this I'm doing this is an important point really doing a function with exponent the base is e Euler's number and at zero that is a I got a touch screen here at zero it's equal to one that limits equal to one so the derivative of the exponential functions equal to the exponential function it is unique in that way it's extraordinarily useful in that way for one thing there are tricks like you develop moments what are called moments and dealing with statistical functions where you take the derivative of e to the or exponent of tx and with respect to t and that will be and then set it equal to set t equal to zero for the derivative and that will give you x it's something I want to mention it's more than I can get into it in depth in this discussion but I wanted you to be aware of moments and I'm going to mention it again later let's look at the logarithm derivative and this will come full circle here a little bit if you take the logarithm derivative you come up with the log the derivative of log is of any base is one over x times so that's that's important and remember of course and times a limit keep touching the screen the limit here should look familiar to you a little bit ago we did a limit of one plus x to the x and it was equal to e that basically is e so you have the logarithm of whatever base to the number e of the number e or just 2.7 1828 1828 45 90 45 23 okay if that happens to be to the base e e to the exponent or the logarithm of e to the base e is one so you end up with that limit becoming inconsequential and taking the derivative so this is one reason why we use exponential functions because the derivative of the exponential functions equal to itself and we use natural logs because the derivative natural logs is x is one over x and of course they're inverse functions just like when you have um linear equations y equals mx and the slope of x equals something of y is one over m the slope of the of the reciprocal of the natural log is related to the exponential function slope or or derivative in other words the derivative of an inverse function is the reciprocal of it okay here's a picture of Euler I have a collection of some of these lithographs I took pictures of and Euler was blind in one eye he spent most of his career in St. Petersburg and he was probably the most prolific mathematician in history but he was not so rigorous if you do an application of binomial theorem which I'm going to talk about in a minute to this log to this x this one plus delta x over x to the x over delta x you will come up with this expression of I keep hitting the screen sorry this expression of E in an infinite series you can also get that by simply deriving the McLaren series for exponent of x and setting x equal to zero I thought this might be helpful for a couple reasons one it emphasizes how you can explore some of these functions you might have forgotten that you have heard of before or that you wonder about by going to google and type in log x comma natural log of x comma and x minus one and x and the green line is x it's color coded the orange is x minus one and the natural log is the red line that I should use a pen or something to meet with I want to emphasize a couple things I know you can't see my pen but anyway the upper left hand corner on the graph is a way of expanding the whole graph you click on plus or minus above and below the cross hairs there or to the side there you click on it it'll show you vertical horizontal axis separately and let you expand either axis and I think for teaching or just use to explore mathematics for any age this is really incredible to me I don't want to see how long I've been doing this but I'll say that people like Euler he was able to do these series in his head to go out a great many terms to get an estimate he could look at a thing for a moment and know if it was diverging or converging and now you can just do it in the computer so you've been Eulerized one other point besides encouragement to use this graph function in Google which I just happened to come across and I hadn't come across anyone else that knew about it so I wanted to emphasize it to you folks is if you look at the red curve which is the natural log and the orange curve which is x minus one so I just placed the green line over by one it's at a tangent there and the natural log the derivative of the natural log is one over x and a one one over x is one so the slope to a tangent of the curve that x equals one should be or a straight line you know approximated at that point should have the slope one you see it does I think it's really important to um I'm tapping I'm sorry and I would I hit my computer with using a pen with it and tapped on the screen apologize for the noise at any rate I think getting a sense of real life experience with what happens with functions you can't break these suckers you can do whatever you want to them you won't increase the carbon footprint you won't hurt the world you won't kill animals no animals were injured or harmed and they're making this presentation now you can do all this stuff pretty safely it's probably quite economical for your own budget as well so any rate here again I just wanted to show these inverse functions now I better pick up speed this is Pascal he's on my wall in my dining room it's one of my collection he was something of a father to probability theory in the early points of it and here's Pascal's triangle which actually goes back to ancient times at least ancient persia if you look at this triangle any number is equal to the sum of the two numbers just above it and what I would encourage you look at each row as the first row is zero the second row is one the third the third row will call two and so forth you number the rows from zero and you number the items zero and one for the row one number across from zero up and number down from zero up if that makes sense I don't you can't see my cursor on my computer can you I'm sure you can't any rate of what you imagine if well take the number four there that's for the fifth that's for n equals five and that's for k equals two k being this I'm sorry k equals one so it's the fifth row first term one is the zero term this relates to compensatorics and so the four is basically would be written five items combined oh let's see if my signal is right you have zero one I'm just taking k times combined in k and items combined in k ways k at a time okay zero one okay five items combined one at a time I think would be five I'm going to go on I'm getting myself confused my point though was that if you are looking for the combinations of anything it would be all the combinations taken at the the combinations have been things taken k times without concern for order would be the same as the combinations for n minus one times taken k at a time plus the n minus one items taken k minus one at a time because each of those ones that are taken k minus one at a time get get a new one wouldn't you go to the next row anyway I've twisted my tongue here somehow and I'm going to go on though because I've got to cover some stuff here Pascal's triangle I took excel and graphed it and this is a I think an important slide for you if you look at this does anyone notice anything about the shape of that curve uh plotting out uh Pascal's triangle as those numbers get larger those curves become more and more like a normal bell shaped curve Pascal's triangle is the spine of the normal distribution in a sense there was a Abraham de Moivre who uh was the first to recognize that a normal distribution could be used to approximate a binomial distribution especially when you get into larger numbers and uh it's tedious to work with binomial distributions so if you get into because you look at the coefficients uh I had meant to talk about in factorial here in factorial is equal to itself times every number less than itself down to one and zero factorial and one factorial or one those get to be really large numbers to deal with if you're working with pen and pencil that's going to be a lot of work and take down a lot of trees so using a technique for approximating binomial distribution with normal distributions becomes quite useful if you need to do that um also just I wanted to emphasize this again in functional analysis if you look at take the logarithm of in factorial you break that product up into sums and if you consider instead of n you kind of imagine it on a a graph instead of n think of x and um do it as though you're uh doing an integral of the logarithm of x that's solvable and that is a little direction for you and how you can derive what's called Stirling's approximation again de Moivre uh was the first to come up with that although uh Stirling improved on the constant and he was English so it was named after him de Moivre was quite interesting he was a Huguenot he had to flee he was put in prison for a while he never married he was a bright guy he had to leave France because of the persecution of the Huguenots and the Protestants French Protestants and he went to no de Moivre was French and he went to London and he studied all the time he did tutoring of wealthy people someone actually gave him Principia that Newton had published and he would take pages tear pages out and read them as he was going to his next job tutoring and I heard that it just broke my heart to think that the book being destroyed but that was the only way he would study it page by page and he found it to be much deeper than the other books he had read uh in any case there was a story also that Newton had people come up to him much the way Brahms would have people come up and want to show their scores that they'd come up with and he would see musical cliches in them just by looking at the score Newton would have people come to him at all kinds of times wanting to look at some problem that they had worked on and he was supposedly quoted as saying might want to talk to de Moivre about that he knows more about these things than I do so this is a graph of the sterling equation where I put x instead of n just to show how fast that grows okay and if you change the scale this is for the x-axis spread out pretty wide so you're seeing just in factorial estimated at the low numbers if you go to a higher scale look at that caveman go he flies all right permutations I want to just point out one thing about permutations and you can look at this kind of a graph you probably or table you've probably seen before about how you get a formula for permutations have been things taken k times that is related to the binomial theorem this is the coefficient for binomial theorem and if you look at the factorial over n minus one factorial there that's of course you have many more permutations than combinations because combinations don't care about order and and permutations are ordered sets so how many more k factorial so I thought that was rather interesting and Newton during the plague came up with a generalized binomial theorem which I wrote there at the bottom which has these equations but at any rate if you expand the permutation thing and Newton's Newton's numerator is equal to this version of the permutation number and the networks for hmm here we are that works for using binomial theorem to do almost any kind of rational exponent okay so I don't want to dwell on this too much here just showing the expansion of the binomial theorem this is a hubachian lithograph from about 1729 that's on my dining room wall that I share with you that's Isaac Newton of course okay the few definitions experiment you make observations one and only one outcome and when you do an experiment your um taking samples from uh that correspond to points in a sample or outcome space and there are different ways of talking about this as I wanted to point out also this uh the two dots and equal sign is uh one way in mathematics that people use to say is equivalent to or uh defined as so it's a kind of shorthand if you ever see that discrete sample spaces are the easier to talk about there's a couple reasons for this I'll let you read this as I talk but when you have a discrete sample space all these finite points that were accountable infinity which means that you can put them in one-to-one correspondence with the natural numbers one two three and so forth events an event is any subset of a set now especially if you get into the continuous numbers uh if you talk about uh all the subsets of the real numbers you're talking about sets of cardinality that are greater than the real numbers in other words there are different levels of infinity the real numbers have an infinity that's infinitely more than the infinity of the natural numbers so you have to be careful with the definitions in terms in these or else you'll get into the same trouble that set theory got into not what like with Bertrand Russell's paradox which is equivalent to if god is all powerful can he invent or create an object that's too large for him to move so you have simple events single sample point and uh all right I threw this in just for a laugh well if you feel this way at this point sorry it stood me right here's one point I wanted to really emphasize expectation is a term that's used a lot in statistics and they talk about expectation if you're you I haven't really defined it yet mathematically but let me point out if when when it's applied to the average or mean or and there are a whole bunch of different estimates of central tendency in distributions usually you use the average that is what's called the first moment which I'll mention again there I'm not going to talk a lot about moments but it's the expectation of a sample and that's totally linear meaning that if you multiply something times that you can take the constant out of the expectation and if you are adding two random variables the expectation is equal to some of those two I think that you need to play with the stuff to really start thinking of it in terms of expectations rather than it's almost like algebra of samples I don't know I got this far down here seem to I don't know but just lights that I'm not seeing okay well I'm going to go with the flow here the weak law of large numbers was worked on supposedly for about 20 years by Jacob Bernoulli or Jacob Bernoulli and who was a Swiss mathematician and physicist and I can believe it probably took him 20 years there were a lot of points that were confusing to people about probability when this all started and he was really looking at coin toss but the idea of it is when you have a sample you get an average there's no guarantee it's going to be the average of the big picture the average of the population but as you take bigger and bigger samples or more and more samples it will start to average out you'll start to get the true mean and he actually proved it you take a bunch of independent variables you can add them together and make another independent variable like this and for some reason a whole slew of my slides disappeared so I'm not going to get into the details there's a point about variance variance is equal to the expectation of the difference between each independent variable and the mean squared it's it's it's not linear like the average is so if you have the variance of these independent variables all being sigma squared and you take one over n that one over n becomes n squared there this is terrible I wish I had the slide created to show the basis of that but it's a tricky part of this proof that but let's you end up with this equation at the lower left hand corner which is based well I'm waiting for this to res now I'm sorry this is really all over the place I'm going to just wing it here here's the idea of how the law a weak law of large numbers was can be proven you have a a theorem called Markov's inequality and it works for any any distribution and it basically states that the chance in a distribution if the chance of a value being an outlier or greater than some value a is less than whatever the average is or expectation for that sample space divided by a and that's really beautiful now that only applies to positive distributions where there are no negative data points if you apply Markov's inequality to Chebyshev's or I'm saying this odd to get Chebyshev's inequality you apply Markov's inequality to variance and you can show that the variance is that basically it puts bounds on the difference between any any x in your sample and the the mean and you take that and then you can prove the weak law of large numbers by based on a limit see if I can get back a little bit here I'm running short on time and I wanted to leave a few minutes for questions if you had them something funky happened to my slides here I don't know they I went through them last evening and they were all in order thank you day but see if I can get anything okay okay here are some maybe I can still teach another point I hope this is by the way if you saw a picture of Prince here I was a joke I was going to talk about the prince of mathematics which is Gauss yeah they were all numbered properly last evening and I looked and I thought they were there added a few at the end that were also numbered right but well I created this scatter graph using excel I just made up numbers it's like bad science and if you look at this this is like what you're trying to what you're trying to figure is is the mean and there's a normal distribution embedded in this it's like trying to measure the position of a star and there are derivations Gauss really was the first one to get a good breakdown of this and there are cool ways to derive the Gaussian distribution and we're done by Maxwell and Herschel and others in any rate a couple of points the there's symmetry radial symmetry it's if you look at any point around the origin 180 degrees from it should have the same likelihood of having a point so you also have x and y and they should be independent variables and of course the radius to any x or y point is the square root of the sum of the squares but you need to separate these out somehow now I wanted to point out if you just play with equations on on google graph like 1 over x that has a curve to it if you could switch it around somehow maybe that would work but no that's not too good for one thing it doesn't it's as a discontinuity at zero you look at this other ways of how can you get rid of this square root of x square plus y squared you need to get rid of the radical maybe in square x squared put it in 1 over x square that gets rid of the radical but that still is this hyperbolic sort of configuration and it goes to asymptotes so that's that's clearly not going to get you what you want in terms of the shape of the function and here what if you just take the exponent of x squared that flies high in air on each side pretty quickly and it doesn't graph very well well what if you do this you know with if you got to go through x equals zero and you're dealing with a reciprocals one way to deal with that is to make it an exponent to the negative x because the negative exponent makes e in the denominator and so negative x and then you also have x squared and you get a curve that looks like this so it looks quite a lot like those little ribs on the growing Pascal triangle that I mapped out on through excel if you can see that just intuitively so I'd like you to remember is that for the Gaussian distribution the exponent to the negative x squared is fundamental to its setup the other thing is if you've got x square plus y squared you want to separate them you've got exponents you look up the left hand corner here you can turn it into e to the y that's supposed to be e to the x times e to the y it's good it's not a book or here we go like this so I want you to remember that the shape of the normal distribution relates to exponent of negative x squared and here is the equation for it all worked out once you set up constraints about symmetry and how the variables act you can come up you can come up with a problem to solve which is not easy to demonstrate it's multivariate integration so it comes out to this equation but you notice you have your x minus mu which is mu is the average squared and by putting it over whatever the standard the standard deviation squared or variance there it normalizes it in other words if you take this and plot it as a distribution and figure the variance of it the variance will be one and it will be centered because every x doesn't matter what equation you start with the every x would be subtracting the mean so the mean of the transformed one is in the center it's zero and you can substitute z is equal to your variable minus the mean over your standard deviation and you'll come out with a useful equation that can be integrated to get you the area under the curve and this is the form you go you put your data in this form you go to your tables and you can extract what you need finally I've just mentioned and I'll finish the central limit theorem is really very cool it doesn't matter what kind of distribution you have you can have any distribution and do experiments and try to determine the mean and as you do more and more experiments to determine the mean the distribution of your plot of the means derived from each of those experiments is a normal distribution that that's pretty stunning really and again it doesn't matter what kind of distribution it is there's one more aspect here I wanted to suggest you try to know the empirical rule that within once it's really standard within one standard deviation of on either side of the mean 68 percent of the data lies the probability that is 95 percent that any point of data will be within two standard deviations and it's 99.7 percent within three standard deviations so 68 95 99.7 that's the empirical rule that's worth remembering so okay we're over three standard deviations from the origin here I had created an equation which was a polynomial which by setting roots equal to zero and one it it crossed the x x-axis at x equals zero and one and it had a skewed quality to it and I was pleased to make it and I normalized it I took the area under the curve and divided it divided the polynomial by it so that if you integrate that polynomial between zero and one it was equal to one and that's one of the slides that got lost here was the axioms by which probability is defined everything has a probability in your sample space of zero or greater and the total probability of all the elements or our points in your sample space is one so if you have a probability distribution curve of which if it's discrete you call it a probability mass function it should total one and I'll give one last tip here it was a great article I read recently is about David Hilbert who died in 1943 in Germany he was a famous 20th century mathematician and his 19th problem he proposed which was solved 10 years later related to you know squares if you look at variance is equal to sums of squares in this case the square of each x minus the average so it's got to be greater than zero and he wondered if polynomials that are never negative are always sums of squares of polynomials and two polynomials squared would equal the original polynomial if you know it's positive everywhere and that's happens to be true that's being used in driverless cars to create barriers for where the car should go and where it shouldn't go it stays in the negative areas then it won't hit any of those positive polynomials it's the trouble was it was too much calculating even for computer you know with pencil and paper you may think you can do a lot and you can use a slide rule and it helps you if you've ever used a slide rule if you get a calculator you can do quicker and more precise calculations probably and you got a computer laptop you can do great things but that expands your horizons and at some point you realize that you're out at sea in a canoe your laptop is like a canoe and you can have equations and problems that your laptop will never be able to get through but this these two people developed an algorithm by which it's so like fast 4a transforms they could work through this problem at any rate there's a lot of mathematics about squares and sums of squares and variance relates to that and i had someone recently asked me why wouldn't use use absolute value for variance and the reason is because it's not useful you could you can define anything any way you want and it'll come out any way you can find relations so but with variance defined as the sums of squares of the difference between each sample value and they mean it's it works and it's useful and you can do a lot of mathematics with it i'll say one other thing real quickly especially with discrete problems like tossing a coin it's another thing i'd shown in the slides which got lost that the probability if it's a fair coin if chance of hitting heads or calling it success and tails fair would be 0.5 and the probability is 0.5 well you never have you know 0.5 isn't a choice you toss a coin you get a headset that's one that's a success and payers is zero and so the mean doesn't have to be part of the sample set as a point i wanted to make and kind of related to that i thought was the idea that half the on the average human beings have one testicle or pretty close to it the average doesn't have to actually be represented above the sample so i put a pdf of my whole set of slides that should have shown at this link that people are welcome to use and i'm going to post it right now along with the article about um uh helbert i was reading something else this morning in 1934 david helbert was having a meal with a man named roost who was the nazi minister of education and so roost asked uh helbert so how are things at gertigan gertigan was the top place for mathematics in the world at the time this is 1934 and that's where gauss had been and in any case he says so how are things at gertigan now that we've eliminated the jewish influence and helbert said there is no more mathematics at gertigan so education and freedom of thought and it doesn't belong to any ethnic group and it doesn't belong to any demographic it's human and it's a treasure and it's one of the things that i think makes it is redemption for humanity which is otherwise seems a pretty sorry lot so i'll end with that any questions i apologize my slides got buggered up so badly i don't know well thank you thank you well i wish everyone a good weekend i appreciate that just it was um i think an ambitious presentation but uh i thought i could fly through it but remember binomial theorem and normal distributions are related and play with graphs say graph whatever on google search and see what happens that looks like a good probability that of having a good weekend i appreciate the opportunity to speak here i'm going to turn my microphone off i guess thank you i think you have a point


I do not have a new computer. This is my old Sony Vio laptop. It's a Pentium-ish machine and tender to run Windows XP with half a gig of RAM and a 40 gigabyte spinning disk. I've had this for years. I can't even remember where I got it now. But recently it's been sitting on a shelf due to having broken down. It's suffering from two problems. One is that the CD drive has failed and it'll only read the inside tracks of the disk. And given that its USB is too primitive to boot off, this is a bit of a problem. The other is that it's been randomly shutting down and the amount of time it's been spending actually running has been getting smaller and smaller until recently it's only been able to power up for a few seconds and then turn off again. Of course, now that it's been sitting on a shelf for six months, when I tried it again just now it worked absolutely fine. But I believe that what's wrong with it is that the thermal paste connecting the CPU to the heatsink has dried out and gone brittle. It's not making proper thermal contact, which means that the machine is overheating and powering off to save itself. So I am going to try and repair it. This is actually the second attempt at this video. The first one I spent ages trying to figure out how to dismantle it and eventually did so up to a point. The point was when I discovered that in order to get to the D drive, which is here, you have to go down through the top and remove the motherboard, which is insane. It's a bit like having to remove somebody's brain in order to fill one of their teeth. I was originally thought that you could go in from this side and lift the back off, but no you can't. So I did a bit of research and I found some not instructions but schematics showing where all the bits fasten together, which is about as good as I'm going to get. So well, I have some thermal paste and a replacement CD drive that is branded Lenovo and has a different shape front panel so I don't even know whether it will fit. But the only way I will find this out is to actually get down to the drive bay and give it a go. So that is what I'm going to do today. So anyway, first step, take the battery out, which is an ancient lithium ion thing that hasn't held a charge for a decade. And I do need to make it absolutely clear that this is not a tutorial video. I know how to do some of this, but when we reach a certain point it's going to be exploratory surgery. So anyway first step is to remove the keyboard. To do this, you undo one screw, find the schematic this screw, B1 which holds the keyboard on and it's a long one at which point we can open it up and we push the keyboard to the left and it should just try not to, it should just lift out or try not to actually break it. And it is fastened to the motherboard by this ribbon connector and it's got one of these tension bars so we flip the bar up and the cable just lifts out. And whoops, got the control key, I wanted that. But anyway, you can now see how the keyboard works. It's a rubber dome with some nasty thin stabilizers. It's not a great keyboard. There we go. So I'll just chuck that aside and this shows the user serviceable bits at the top, which is the RAM in this case. This machine reports 512 megabytes of RAM which is a decent amount for a machine of this age. If I had discovered how to do this when I ordered the CD drive, I would have bought another memory module. So now we go down to the bottom and we're going to remove this hatch. This is the service bay for the hard drive. Unfortunately it doesn't actually show us anything else that's useful, but we have to take this off anyway. It's a very weird combination of easy to maintain but easy to service in that you can actually take all the bits off and there's nothing glued down. Well except for one bit which I'll demonstrate later. And completely maddening. That's the other long screw. Okay. It just lifts off. Exposing. Here is the hard drive. Here is where the CPU is. This is the heatsink. It's got a thermally conductive pipe. The heat pipe, that's what they're called, which connects the CPU to the cooling system. This is the radiator and this fan blows through it. So this is one of the bits I'm going to be taking off and repasting. But I can't do that until I can take the board out because actually I might be able to you know. I thought this was all one piece but it's not. It's just stuck down. Okay. Well we have to penetrate down this far in order to get at the CD drive which is here. So let's move the hard drive. Which we do with these screws. Just those two. And then the caddy lifts off and unplugged from here. So that also goes aside. And this reveals not very much but we have to get that off in order to take the motherboard out. So the next thing, this is where it starts getting a little bit unknown. Is to remove all the screws that are helpfully labelled with these arrows. Indicating their fixing points. Oh yes. This is the bay connector for the docking station. Which I haven't found. This machine actually has a decent number of ports. So on this side we've got USB PCMCIA, FireWire microphone and headphone VGA. And on this side we've got another USB modem and ethernet. And a memory stick pro slot for anyone who remembers that. So it's actually quite well specced for an XP grade laptop. I'm actually planning on putting FreeBSD on it. For use as a very low end build box. Making sure that my programs actually work on FreeBSD. If I could get it fully upgraded RAM wise then it would be really quite nice. So it also has a layout shape that means that you can't actually tell what is the front and back anyway. So we are next going to want to remove this panel. This is connected to the motherboard in various ways. One of which is this connector which is another tension bar. So lift the bar and pull the thing. There's these two which are even cruder than that. You pull the blue tab which wedges the ribbon in and it just lifts out. And this one which is the power connector. So we remove the screw this is for the ground wire. Well earth really and now I need to find my favourite pair of corner nose pliers which I always have out because I use them so much which means they are never where they are supposed to be. Yes they were hiding under where I put the keyboard. Okay so now we want to remove this which is the power connector preferably without breaking it. There we go. That connects to this barrel connector here. Okay. I'm trying to remember what happens next. I think now is the point where we start spudging. There's a lot of little plastic clips. Hold it up. Hold the top on but yeah I remember this bit. Sorry this is hopefully see how to focus because it's so close to the camera. But the knob that holds the PCNCA card the eject knob of the PCNCA card actually stops the top coming off which I've forgotten to screw. I think I have forgotten to screw this one which I believe. No that wasn't in fact it put that back in again. Okay let's try prying the top off. So I've managed to unclip it around here and it's dropped back again. It's clipped back on. Right something is holding it on. Yes when you move the lid like that and you have your finger in there it actually traps your finger. It does feel like something is binding it down here. So I know it's not that screw and I know it's not that screw. And I'm pretty sure it's not that screw it's a long one or a short one. It's a short one. The long ones go all the way through and connect to the top shell. There's more the short ones just hold bits of the motherboard together. And you can see that there's at least three different levels. This, this, this but there's also tools which are visible from the other side once I finally managed to get the top off. Naturally there we go. It is holding this down. There's a thing in there. Yes this, the barrel connector for the power is attached to the top and needs to unclip. Okay so it's only attached in one place now which is in the middle. Right I can't demonstrate because I can't close the lid at the moment but there is another screw not there in this hole which holds the top on that screw. And hopefully that was the last one and off comes the top shell. Right all except for the Modem clip opens right and it is free. All except for this. Which holds the, well which connects up to the speaker. There is only one speaker. No I tell a lie there's another speaker up here. But I'm not sure. Yeah that's connected up via this which also feeds the three LEDs here. Now I do not know how to get this off. I don't even know if it's a socket or a plug or whether the wires just push into a friction fit thing. It does look like a plug of some kind. Oh right it just pushes on. Fantastic. Right we've taken the lid off. So on this side on camera you can see the touchpad mechanism and its buttons down here LEDs for the power and Wi-Fi lights. Interestingly the Wi-Fi switch is here but there doesn't actually appear to be a switch behind it. Which is interesting. Over here we've got the memory stick reader and its wire. Speakers here and here. Here's the little PCB which connects to the other speaker and has the LEDs on it. And we don't need any of that. And this is where I got to last time I tried this. So we can see here is the Wi-Fi card which is a PCIe thing. This I don't know what it is. Some mysterious daughter board. This is the backup battery which doesn't appear to have leaked. I'm not really a fan of these but it's glued quite firmly onto the motherboard. This is part of the cooling mechanism. In order to get that off I probably have to remove this metal bracket. Here's the PCIe slot. This is the bottom of where the CPU is. So here we have all the power conditioner caps for the CPU itself. And this metal frame is what bolts it to the motherboard. So we're probably going to have to remove that. Sorry what am I saying? Not to remove that. We don't want to remove that but we do want to unscrew the heatsink from it on the other side. We do want to leave the CPU on the board. So here is the schematic for the board. So here is the PCIe. Oh yes here's the antenna cable which goes up into the hinge mechanism and it will be up top of the screen. The actual screen cable I think is this and connects to the motherboard here. And there's the battery connector. Yes So I think that I do not need to remove the motherboard in order to remove the heatsink. Because I think I can get at that from the other side. But the CD drive is under here. And it is fastened in with some side on screws. There's one just in there. But there's another one about here as well. These two screws it goes like this. And this plastic bit sticking out I'm really not sure whether there's room. If I turn it over it goes here. So we'll see once I managed to get the CD drive out. There's also a screw here in there. But I don't know whether it's actually done up or not. I can see the two end on screws. This one from the other side. This one is in there. You might be able to see it shining. So I was thinking that I might be able to remove the heatsink. And that would give access to the screw that was in here. And this screw I might be able to get access to this way somehow. But it's behind this plastic thing. I'm peering down the PCM and CD slot. I can't see it in there. It's ridiculous that you have to remove the motherboard to get at it. Because it's a replaceable moving part. Okay well assuming that I am actually going to have to take the blasted motherboard out. See, yeah. See here's the hinge. The laptop hinges have to take a lot of force. They're pretty solid. And it is fastened to the plastic shell which now I think about it. I don't think it is plastic. I think it might be a titanium or aluminium. Yes apparently it's metal. I found no instructions on how to do this other than those schematics which aren't very helpful. Okay well anyway let's start with the PCMCA slot. Because this is sitting on top of the motherboard. So this is probably a good bet. PCMCA slots are increasingly rare. But they're actually quite valuable for certain machines. So I really want to have a Linux machine or a BSD machine that's capable of accessing them. For example memory cards for like my NT200 PCMCA. So it slides out like that. And this bit should then lift off. It's fastened down by this metal piece. Which again has this screw. Yeah I'm not sure. You can see the arrow here. I was worried it was actually pointing in the other direction was at a screw that I didn't have access to. I really hope this thing will still work once I'm done with it. Okay so we could unplug this but I'm not going to. Because I'm not terribly happy about putting those screws back in again. Do you want to get under here? Okay well they have thoughtfully marked the mount points. So I'm assuming that if I take all these out it should lift. What's this? Interesting. This is a screw from the other side under here somewhere where it's completely inaccessible. Here's the front bezel with the switches and things on it. So you can take that off by undoing this screw. We are going to have to do that at some point. That screw is seized. Yes because this is screwed to the chassis I am going to have to remove it and unplug it from the motherboard which is this. So let's just do that. So one of these tension bars has been taped down. It slides into the connector and then the tension bar pushes in and locks the cable in place. Okay there is some more tape we are going to have to remove at some point. There is another of these. Oh interesting. The CD drive is not coming with it when I pull this. So what is holding it down here? I think these screws, quick look at the bottom. I think it's now these. So let's remove them and see what happens. Certainly feeling limbsier. I need to find a way to re-magnetize my screwdriver. That hasn't done a lot I have to say. Well there are a couple of screws here marked with arrows. Now this is the daughter board. This isn't attached to the mother board except via the cables. That's another daughter board. Let's take a look at that schematic. It's not very easy to follow I have to say. So here are the mounting screws. This metal plate is this. Fastened down it says by three B6's. Which are these? What is the bottom of this Fasten 2? There is something between that daughter board and the PCB which is probably interesting. I don't know what that's Fasten 2 but let's take them out and see what happens. Luckily most of the screws are the same. Oh and I completely forgot about this one as well. The seized one that's not going to help. I need the big screwdriver. Which I don't like using in this small stuff because it provides way too much torque. Not putting that screw back in again. Now what happens when we lift? It's still fastened solidly down. That's not coming off at all. There it is. The tape's not helping. So what's underneath it? RF stuff? Yeah. There are some metal standoffs which connect to the daughter board below. This one is mobile. That one is part of the fan. And this one just connects to the the heat sink the CPU mount there. So I actually want to put that one back on again because I don't want that standoff to go astray. So I want to fasten this down to here. Which is connected to the bottom of the mother board. So this isn't actually locking it onto anything other than the mother board. Which is what we want. And here to connect it to the standoff. And do I want to fasten this one on as well? I believe that as it's connected to the fan which we're going to leave in place yes let's put that one back. So this should now, it does feel floppy than it was less floppy than it was anyway. There is something fastening it down over here. I don't believe there's a screw under the RAM but let's just pop this off to check. Nope there isn't. Well there aren't any screws accessible here. So I wonder where to go next. I've removed all of these except for holding the heat sink on. We are going to have to remove those eventually. See it's not connected there anymore. There's something over here. There aren't any holes under these stickers are there? No. There's a single screw here which appears to be connecting a couple of bits of chassis together. But I don't think that's particularly relevant. Is there anything under the PCIe card? No. Having this as a card by the way is really useful because if this machine ever becomes defunct I can rip it out and use it in another machine. Okay let's take a look at this.  Here is the PCB with a little notch there. Here's the spreader and radiator which is on the other side. Here's the top of the radiator. Multiple door to boards. There are a few upside down screws. I think I've got them. Oh there's a screw in there that's holding the fan on. I'm not sure I want to try and take the screen connector off. There are no screws there. It doesn't feel like the fan is actually attached to the chassis. It's quite clear now that I'm looking more closely at it that this is the metal chassis and that the bottom case is attached to it. So here's the chassis but here's the plastic. Oh that's interesting. I think I was actually completely wrong. It's probably not in focus but you can tell here, here's the plastic of the case and here's the thing I thought was the chassis. You see the light grey line that could be metal treated plastic actually for presumably RF shielding. That's the only place I really haven't looked is under the feet. I don't think there is anything there. I don't want to take those off. I'll never get them back on again. I wonder that feels very solid. There's no flex at all because it's got this whopping great chunk of metal on the other side. I can't think of anything that is still fastening this thing onto the case. Am I just not trying hard enough? This definitely feels like there's something here holding it down but I have no access there. So how can there be? So here is the bottom. So here is the CD drive and you can see oh look there is a screw going in there. It's this way up. It doesn't appear to be a corresponding screw hole on this but that B11 matches here. There is the switch panel hard drive bottom hatch. Here is the actual plastic base itself. So here's a screw which I think is this one. Here's a screw which I think is this one. There is a metal box on the other side that this is screwed down into but that's coming out with the PCB. Here is the little empty box in the bottom of the case which I think appears somewhere here. I'll just double check that. It's this thing. There's nothing in it. Oh that's interesting. There is actually, it's had access to the inside and I'm genuinely not sure but I think the purpose of that box is to support the PCB under there. So that'll be about here. Here is the hole for the bottom hatch, this thing. And there's a standoff next to it there. Here's the sliding hatch for the docking station adapter. Sorted bits and pieces for the battery mechanism. I think I am going to have to try and remove the heat spreader. Honestly I was hoping to get the thing out of the case before doing this. I mean I'm going to have to anyway but this appears to be a part that Sony thought was user serviceable otherwise it wouldn't be accessible from the quite big hatch. So this is the part that I think was causing the mysterious power-offs. I think that the thermal paste is going to be dry and gunky. But it certainly wasn't stuck down very much. Ooh there wasn't really any thermal paste. And that is indeed dry. Huh. Okay. Well that would be easy to fix. Yeah look I don't even have any thermal paste in my hands. And here is the CPU itself an Intel. No other markings. Yeah that heat paste is useless. So what has that exposed? We've got one of the CD tray screws. But that won't really help because we don't have access to the other one which is in there. You see that this metal bracket these four screws were holding the heat spreader on. These two screws were holding the bracket to the PCB. That hasn't made anything else come loose. I can see a screw just in there. But I don't think that part of the I don't think that's holding anything to the chassis. The fan looks commendably clean which is nice. I was wondering whether I'd have to blow fluff out of it. Oh boy. The fan is big and metal. You see there's a screw there. That could be going through the PCB and into the chassis. So that would be around here somewhere. There's nothing shown. Let's find the main board. It would be around here. There's nothing there. But let's try it anyway. I'll take it out all the way. Yeah, it made a huge difference. That tape. This is the plastic grill that goes on the front of the radiator. This is being held in by the screen cable now. Okay, I am going to have to unplug the screen. I have a key remover here which may work. Yes, that is working beautifully. Okay, we've now got the antenna cable in the way. So let's remove this tape. We're not going to be able to stick these back on. I don't have any cap to hand tape. I should order some. Okay, this is just copper tape. Okay, now does this want to come? Get this plastic guide out of the way. Okay, this cable is now in the way. So we can unplug it from either end. But this end is easier access. It's coming. It is actually coming. I'll just remove the front bezel for the CD drive just on clips. I think that the mother board wants to be disconnected from the CD drive chassis which will be this screw. Yes, it does. But there is still something holding it down. It could be the CD drive connector. There you go. And this folds out of the way revealing the CD drive.  All right, now it lifts out. Oh, that's interesting. Oh, God. I think that I could have just undone the appropriate screws, leave it carefully in the right place, and the whole caddy would have removed, would have slid out. And I wouldn't have perhaps have done any of this nonsense. It'd be these two screws here but there is nowhere to pull on this side in order to take the thing out through its slot. Now the whole thing is so back heavy. And let's just compare with this drive. You notice that these are not the same connector. You know what? I'm going to leave that for now. Because now I'm going to start reassembling it. So this cable plugs in here and the tension bar does up. Okay, this plastic thing here is all hooked in the wrong place. So we plug that in. This thing over here is in the right place.  He does yes. I was wondering if this is slightly bent. I'm wondering if this was supposed to go inside this rail but no it doesn't. On, go back in. I have a lot of screws on my workbench and I would rather like to get most of them back into the laptop. I actually still have some screws left over from the test assembly I did the other day. The problem is this metal piece was bent slightly so it's not actually lined up anymore. It'll be fine once I get the screw in. Let's fasten the PCMCA tray down. A bit of little screws. There we go. Odd little detail. There's a red splodge of ink right over the O of Sony. I have no idea what that means. Okay, and I do actually need to put this bit in first because this is supposed to tuck under the PCMCA stuff. Before I do it let's just route this back in. It's like Lego but with worse instructions. Where does this go? Oh, did this go in? Yes, it was here. No, it wasn't. It was there. Okay. One screw there. This one holds this ground wire in place. This one goes down here. So it should go in here. I'm going to assume that these screws go in the obvious places. I've completely forgotten which ones went where to be honest. Luckily they're mostly the same. There are like three different lengths and a few different colors but I don't believe matters. And two different threads. There's a small thread and a large thread but it's mostly all the same. Okay, now before I do anything else, where did that CD drive go? There is one of the screws. It's this one and this one. If you take those two off you can then simply push the CD drive out. That explains why this connector goes in this way rather than down the way the other motherboard connectors went in. Speaking of motherboard connectors, there are actually a few that I believe have gone into place but let's just tuck this. Put this back under the tape. Try and put it back under the tape. I think this is the only one that actually matters because we don't want that cable straying over the fan. That's kind of a mess. It's also not very sticky. We'll call that done. Here is the shell that goes over the top of the PCMCA card. And yes I appear to have screwed this up. I need to take these two screws out again. I need to take the tape where I have to try and remember the order in which I took it apart. Or rather the order in which I should have taken it apart and then reassemble it in that order not forgetting any pieces. Such as for example this piece which is the USB thing that goes here which covers up this. There it goes this way up. And just clips in place. What other bits are there? I think this metal shroud is the only one actually. That goes on here which helps to hold these cables in place like so. I'm going to assume that these are the little screws. I'm very puzzled as to what this case is actually made of. It's either a very hard dent plastic or a very light metal. I think it predates the age when laptops were all made out of titanium and aircraft aluminium. It might just be very good plastic. But these screws are tapped straight into whatever it is. They're mostly going in beautifully. I think we need a screw here. One is a short screw. Screw there. I can feel it hit the bottom of its thread. You don't want to keep pushing when that happens. You never know what might be on the other side. So I had to take a break with my SD card filled up. Anyway we're going to reattach this now. This here by the way is the wireless switch. Let me just double check because that goes here. You see there is nothing behind it for the actual wireless switch. There is actually the top shell goes on like this. The bar ends up like this. I was just checking to see if there was a plastic piece from the switch that was sticking up to this PCB here. But there isn't. That thing is just a clip to hold the PCB in.  It doesn't do anything. Fascinating. It goes on here That thing clips on. The wire down like this. And if I remember correctly this was a small threaded screw. There you go. You do need to reattach the cable. So this, make sure the tension bar is released. This pushes in like this. The tension bar goes into place. The tape sticks down. That's fine. I actually quite like these connectors in terms of nasty motherboard connectors. These are some of the least bad I've met. Alright. What is next? What parts do we have on the desk? We've got the heat spreader and radiator. Hard drive, battery. These go in last. We've got the two CD drives. The new one and the old one. I believe that I got myself a DVD recorder. Yes, I did. Whereas the old one is just a DVD ROM. We've got the bottom hatch. The keyboard. So I believe we've got all the bits. So now let's put the top back on. So this is going to go on here. What cables do we need to connect beforehand? None, I believe. Provided they're all looped through so I can get at them. I think I can just put this on now. I need to make sure that these pieces are done in the right place. The flap that covers the Modem in Ethernet port is attached by a nasty rubber hinge. So that just pushes into place. This should clip down. The PCMCIA thing is in the wrong place. All those nasty little plastic clips that took me so long to take out go back in. Right. Now we plug these back in. Start with this tiny little thing. This should just, that wasn't so bad. Power cable plugs in. Seems like quite a lot of screws left on the desk. Well, a grounding cable. I'm not sure why this is separate ground and neutral wire. And that's the wrong screw. I need a short one. It screws into this standoff that I assume is connected to the ground plane of the PCB. And then these wires hook into these little plastic bits to stop them flapping about under the keyboard on getting there. At a sudden panic moment this is the connector for the keyboard. Okay, let's do this one. Which is the memory stick. Fold up the tension bar. Push the connector in. Fold down and stick the tape down. This one has actually fallen into precisely the right place all by itself. So all we do is we take the stiff piece of plastic and we wedge it in here which locks the cable into place. And likewise here.  Okay, and this wants to go under that plastic thing. Okay. Keyboard. Here's the standoff that goes on here and then the long screw from underneath folds up. And locks it in place. Again, my last strip drops into the connector and I fold down the tension bar. Yeah, it doesn't go in very far, only about a millimeter. Pushes down, gets into place. Done. And it feels very flimsy because I'm done any of the screws up. So let's start with the keyboard. Okay, and let's do some of these up. Some of these were, yeah, let's use the short ones for these. Another short one for this one. We're out of short ones so this one must be a medium.  It's this way. So it goes on like that. We're going to drop the screw in there. That's feeling firmer already. We didn't take that one out. The hatch goes on like this. Just looking for screws inside. I need to do up. I think that's a lot. And put the hard drive back in so the connector just pushes down. Hard drive sits like that. This screw is part of the hatch. So we need to do the others up.  So let's just add a bit of paste. That looks grain of rice sized. It might still be too much actually but we'll see.  I looked up the instructions and how to actually add this place and they said firmly apply constant pressure and you do the screws up in a cross pattern a few turns at a time so as to increase the pressure evenly. But it's really not at all difficult. They said do not attempt to spread the paste yourself. Let the processor do it as you do the screws because that applies pressure constantly and it means that the blob of thermal paste will expand evenly and you won't get air bubbles. That's that. So we can't put the hatch back on until we've done the CD drive. So let's take a look at the CD drive. Here's the Duff one. Here's the good one. Now there is a few mounting racks which we're going to have to take off and move over. So we undo the screws and there's also the PCB adapter in the back that we're also going to want to move over. These are the mounting rails which hold the CD drive into the bay.  They sent me the wrong drive. So I got the drive on eBay and the seller said that it was a drive for one of these and I was hoping that this was going to plug onto a SATA connection there but it doesn't. Let me just remove this and see what there is underneath. Now focused that is focused. Well at least we know it comes off. So I'm going to have to get in touch with them and say oh you sent me the wrong drive. The form factors right as you can see is just that connector that's not blast. Also you notice that the let's clip these back on. Oops that's broken never mind. Also you notice that the front bezels are a different shape. This one's got a gap in it. I was hoping that I'd be able to swap the bezels over and hide the gap because you see the drive itself has the gaps but the button's in the wrong place. The button and the LED are in the wrong place. Okay oh well and I actually appear to have broken the bezel. Never mind. So this goes in here. I need to put the rails back on. This rail goes on here and this rail goes on here and I'll put the whole thing back together and I'll try the FreeBSD boot DVD to see if it works. I suspect that it will boot but will then fail as it tries to load bits of the installer because unless it mysteriously comes back to life due to being on a shelf for six months the way the CPU did then it will hit the problem of the CD drive which is the reason why I wanted to replace it and there should be a screw there but there isn't one which is interesting. Okay it plugs into place and the hatch goes on and I think this is a long screw. No it's not feel it hit something in the other side of the PCB. Oh and I shouldn't put that screw in. With luck I should not need to have to open this up again if I want to replace the CD drive when I get one that works. I just need to remove these two screws. Where did the long one go? I think it was here. It's not quite right actually. If you look here the hole's not centered I think this was the long one. Yeah that's too short if I think this was the other long screw most of this video is going to be me putting in and taking out screws okay and this one and this one and oh there are actually more screws a lot of screws. So it looks like my camera suddenly cut out. I think I need a new SD card but we're about to give it a try. I can't see the screen at this angle but hopefully you will. So I've plugged in my VGA monitor. It's on my desk so we give it some power and power. Well it starts and it is in fact booting MS-DOS from the CD in the drive. So we know it works. Let's give the... I will actually reboot it into the BIOS and make the screen bigger and I will grab the free VSD disk. Okay one free VSD dvdr and actually you can't see the CD drive from where you are which is here. Also remember I said the wireless LAN switch was a dummy. Watch this. I have no idea how that works. There did actually seem to be no switch on the other side anyway save and exit for the slow boot yep and it's failed. So it's enough of the drive is working to have loaded the boot loader but then it has failed to load the kernel because that's somewhere else on the disk. The DOS CD works fine because the data is all in the center of the disk. In fact can you make out the just about looking at the viewfinder. You can see the gap there where the data is. So I'm going to have to contact the eBay seller and tell them that their drive doesn't work but luckily I have some video of the connectors so I have managed to take this thing apart all the way down to removing the motherboard it was mostly a waste of time but now I know how this works inside and if anyone else needs to do the same thing then they can do that and if anyone wants to find out what one of these looks like without taking their own apart. So it's not completely wasted I just wonder how many hours of video this is Well I hope you enjoyed this video and please let me know what you think in the comments