Question: Let X1, X2, . . . , X100 be a random sample from a uniform distribution on the interval (0,1). Let S = X1 +

Let X1, X2, . . . , X100 be a random sample from a uniform distribution on the interval (0,1). Let S = X1 + X2 + . . . + X100.

(1). Find the pdf for the statistic X(1) = min(X1, X2, . . . , X100)

(2). Find the pdf for the statistic X(100) = max(X1, X2, . . . , X100).

(3). Find an approximation for P(S > 55).

(4). Let \widetilde{X} = S/100. Find an approximation for P(2 < \widetilde{X} < 2.15).

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