29. 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,

$$P(X_{(n)} - X_{(k-1)} > t) = (1 - t)^n$$

where X₍₀₎ = 0, X_(n+1) = 1.