(Bootstrap in Example A of Section 8.5.1) Let U1,U2, . . . ,U1029 be independent uniform...

(Bootstrap in Example A of Section 8.5.1) Let U₁,U₂, . . . ,U₁₀₂₉ be independent uniformly distributed random variables. Let X₁ equal the number of U_i less than .331, X₂ equal the number between .331 and .820, and X₃ equal the number greater than .820. Why is the joint distribution of X₁, X₂, and X₃ multinomial with probabilities .331, .489, and .180 and n = 1029?

Reference

Hardy-Weinberg Equilibrium