Suppose $X_1,X_2,\cdots,X_n$ are iid uniform random variables on $[a,b]$, what is the distribution of $$Y_n=\frac{\max_{1\le i\le n}X_i+\min_{1\le i\le n}X_i}{2}?$$
2026-03-29 12:05:21.1774785921
Distribution of the mean of max and min
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