Question: Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [0, 1], and let W denote

Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [0, 1], and let W denote the range of the sample, as defined in Example 3.9.7. Also, let gn(x) denote the p.d.f. of the random variable 2n(1ˆ’ W), and let g(x) denote the p.d.f. of the Ï‡2 distribution with four degrees of freedom. Show that

lim gn(x) = g(x) for x > 0.

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