Let X1 and X2 be two independent random variables both having discrete uniform distribution over 1, 2,.., n for some positive integer n.
2026-03-30 05:12:27.1774847547
What is the probability mass function of max(X1, X2)?
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Since they are independent the event $(max(X_1,X_2)\le k)=(X_1\le k)\cap (X_2\le k)$, which has a probability of $(\frac{k}{n})^2$.