The gist of the video is that if you have three independent random variables, X 1, X 2, and X 3, that are all uniformly distributed between 0 and 1, t

And now it’s all this

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2024-11-30 16:00:03

The gist of the video is that if you have three independent random variables, X 1, X 2, and X 3, that are all uniformly distributed between 0 and 1, then

I should mention here that I’m not using the same notation as Grant. The textbook used in the class where I learned this sort of stuff was Ang and Tang’s Probability Concepts in Engineering Planning and Design. They used capital letters for random variables and lowercase letters for particular values. It’s a nice convention that makes it easy to distinguish the random from the nonrandom. I’ve stuck with it for 45 years and don’t intend to change.

The probability P[X≤x] is a function of x and is known as the cumulative distribution function1 (CDF) of X. Therefore, the probabilities given above are the CDFs of the functions max(X 1,X 2) and X 3.

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. This is one of the great advantages of having so much computing power at our disposal.