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On how to compute the expected max of random vectors

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Tags: programmingstochasticsprobability-theoryanimationpythondice-rollsbeta-distribution

I motivate the formula for the expected maximum among the components of a random vector, each following their own distribution. To this end, I provide Python code animating the empirical order statistics given by the Beta distribution. And this itself is motivated by a dice roll scenario.

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The animated histogram plots are great! You might also try them as a stacked bar chart, so that the colors will appear to partition the rectangle [0, 1] x [0, #samples/#bins] after a while.

I think you glossed over the calculations a bit too quickly, and possibly made them a bit more complicated (e.g. I don’t think you really need to use the log derivative)

Cool video, and I quite like it! I think this video feels a bit long and unwieldy for what it is, but it does feel like it would make a good lecture in a relevant class. I think as web video content it could be improved to be more engaging or dramatic for general audience, but if this is a topic a student is genuinely interested in I don’t think that’s a problem at all.

Beta distribution was not explained. It was also not explained why the graphs detail sampling from a continuous distribution after the introduction used dice, a discrete distribution, as an example. This video felt unscripted, so it felt like a university lecture. The video was not edited to cut out downtime, like when files were loading. Perhaps in the future the images could be pre-loaded into a slideshow program.

4.1

I couldnt understood the analytical part also i needed to watch it around 5 times to get what was going on but yeah it made sense after that so good job , as a first time it was preety nice ! Could surely use some writing while explaining Thankyou for your contribution !