(Bootstrap in Example A of Section 8.5.1) Let U1,U2, . . .

Chapter , Problem 35

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(Bootstrap in Example A of Section 8.5.1) Let \(U_{1}, U_{2}, \ldots, U_{1029}\) be independent uniformly distributed random variables. Let \(X_1\) equal the number of \(U_i\) less than .331, \(X_2\) equal the number between .331 and .820, and \(X_3\) equal the number greater than .820. Why is the joint distribution of \(X_1\), \(X_2\), and \(X_3\) multinomial with probabilities .331, .489, and .180 and n = 1029?

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