Say I have 20 discrete uniform i.i.d random variables $U_i$ with $$U_i\sim U(0, 120)$$ and I am told that: $$\sum_{i=1}^{20}U_i = 1800$$ I want to know the probability that one of the realisations is above its mean given this information, or in other words $U_j > 60$ for any $j\in\{1, 2, \cdots, n\}$ ? That is, what is: $$Pr\{U_j > 60 | \sum_{i=1}^{20}U_i = 1800\}$$
2026-03-25 07:44:40.1774424680
Compute $\Pr(U_1>60\mid U_1+U_2+\cdots+U_{20}=1800)$ for $(U_i)$ i.i.d. uniform on $\{0,1,\ldots,120\}$
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