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Square roots and maxima
A brief numerical and graphical check on a 3Blue1Brown video.
Grant does his usual excellent job of explaining why these two functions have the same CDF, but if you have any doubts, it’s fairly easy to check his work numerically. We’ll generate three sets of n random numbers from the uniform distribution, apply the max and sqrt functions to them, and sort the results in ascending order. If you have some background in statistics, you might be expecting me to run the Kolmogorov-Smirnov test to check the goodness of fit between the sample and the analytical CDFs.
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