Question: Let X(1) X(2) . . . X(n) be the ordered values of n independent uniform (0, 1) random variables. Prove that for

Let X(1) ≤ X(2) ≤ . . . ≤ X(n) be the ordered values of n independent uniform (0, 1) random variables.
Prove that for 1 ≤ k ≤ n + 1,
P{X(k) − X(k−1) > t} = (1 − t)n
where X(0) ≡ 0, X(n+1) ≡ t.

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