CORRECTION: At 6:20 the summation on the left should be divided by N. Also, at 7:49 we meant (-2)^2 and not -2^2. Thanks a ton guys for helping us spot those issues.
At 9:19 The positive and negative kurtosis on the graph should be switched. Also isn't the formula for Variance suppose to be devided by N - 1 at 10:36
I've been looking forward to this episode. It's always nice to have different ways to explain why complete randomness makes it easier to control for extraneous variables. Very counterintuitive
10:54 its the guy and girl from the meme. yes THAT meme. (the one where the guy is checking out the girl who just passed by him while the girl to his right looks disgusted)
Excellent video. Just one mistake that has to be rectified. At 9'03'', the graph illustrating Kurtorsis is incorrect. Re-scaled Kurtorsis is an indicator of heavy tails compared to normal distributions. In that graph, the light blue curve with heavy tails (e.g. a t distribution PDF) should have a positive Kurtorsis, while the blue curve with thin tails should have a negative Kurtorsis.
It looks like variances are different on these, so maybe the kurtosis is right but very hard to interpret because they scaled their distributions to fit in the picture? Wouldn't it be more illustrative to have the same variance on the graphs and only vary kurtosis?
03:00 - best guess about the random process is the mean. 04:20 - Expected value for discrete values. 05:04 - expected value for continuous numbers 05:49 - variance or second moment of the data: E(x-u)² how different data points are 07:17 - skewness or third moment of the data: E(x-u)³ how many outliers on each end of distribution 08:58 - kurtosis or foutrth moment of the data: E(x-u)⁴ how thick the tails are
I'm watching this just before my lunch time. Now I want some french fries... Edit: Yup. Done with the video, it's lunch time - I'm heading to go get fries...
Is really anything random? Like if you could perfectly roll the dice the same way, you would roll the same number every time. What causes “randomness” are variables you cannot control like a gust of wind
Supreme gamer76 Not necessarily cannot control, but cannot predict. Because there are things out of your control which you can predict like an event of a car crash (before a car crash time slows down for the victims after they realise that it is going to happen), to a large extent your height, your IQ, your digestive system operating, heart beating etc. If we exclude epigenetics, your whole genetics are out of your control, yet the way they work to produce proteins and other structures is getting more and more clear every day and therefore, as more variables are getting known, can be used as a means to predict with greater and greater certainty. They are out of your control but you can't say they are random. On the other hand, if you can't predict something that means that either some variables are missing or you don't know how the dynamics of that particular thing operate on a logical level = unpredictable. And at that point you just draw a conclusion based on a data set to infer the chance that you're going to be in whatever category = randomness. That's what I think, but for sure many things that are out of your control are unpredictable as well.
@@MENTIONNN time does not slow down, their perspective of time might slow down, but time itself always goes forward at the same rate. (for everyone on earth going at relatively slow speeds)
*_...nice to have the words, "skewness, kurtosis," but pictures-please, too..._* *_...is kurtosis telling us its modality, hinting that it might-be-multi-modal..._* *_...(higher orders are sensitive to fewer-large values over many-smaller)..._* *_...((but then isn't that 'antiskewness' leaning-to-one-side vs big-strays))..._* *_...((('anti-kurtosis', too-the dictionary says, sharpness, from, bulging)))..._* *_...((((are we talking about the-distribution, is skewed, or the-mean-is))))..._* *_...(((((maybe we should subtract-out variance to calculate statistics)))))..._*
I came here because I thought it was going to be about generating random numbers... Does this have anything to do with the difficulty in generating truly random numbers? Loved the ending.
