Take $n$ i.i.d.uniform distributions. Their sum, $X$, is an Irwin-Hall distribution with support $[0,n]$: $$X=\sum_{k=1}^nU_k.$$ Naturally, the mean of $X$ is $\frac{n}{2}$. What if I am only concerned with values greater than some $a\in[0,n]$? What is the mean of $X$ given that $X>a$?
2026-03-28 22:13:46.1774736026
Conditional Irwin-Hall Distribution: What is the expected value of an Irwin-Hall given that it is greater than some value?
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