Question: 2. Let U,U,,... be independent random variables having the uniform distribution on [0,1]. Find the limiting distributions of the following statistics Y and Z.,

2. Let U,U,,... be independent random variables having the uniform distribution on

2. Let U,U,,... be independent random variables having the uniform distribution on [0,1]. Find the limiting distributions of the following statistics Y and Z., respectively. n (A) T, = [TU, i=1 -1/n (b) Z, 2n(1-R), where R=U(n) -U) and U() is the ith order statistic.

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