Suppose that $x \sim U(0,1)$, then you know that realized value of $x$ is bigger than $a$ where $a \in(0,1)$. Can we conclude that $x \sim U(a,1).$ Intuitively, it seems correct to me but at the same time I also thought about the movie - 21 where opening wrong gate will not give the same chance to the other unopened gates? What do you think guys?
2026-03-28 13:32:20.1774704740
uniform distribution given some information
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You can compute the conditional distribution directly and see its $\mathcal{U}(a,1)$: $\mathbb{P}(X\leq x | X>a)=\mathbb{P}(a<X\leq x)/\mathbb{P}(X>a)=...$