Question
(a) Let U1, U2, . . . , Un be independent random variables, each with the uniform distribution on the unit interval [0, 1]. Let
(a) Let U1, U2, . . . , Un be independent random variables, each with the uniform distribution on the unit interval [0, 1]. Let U(k) be the k-th smallest number in U1, . . . , Un (that is, U(k) is the k-th number in the order statistics). Find the density of U(k) .
(b) Let X1, X2, . . . , Xn be independent random variables, each with exponential distribution with rate 1. Let X(k) be the k-th smallest number in X1, . . . , Xn (that is, X(k) is the k-th number in the order statistics). Find the density of X(k) .
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From Fourier Analysis To Wavelets
Authors: Jonas Gomes, Luiz Velho
1st Edition
3319220756, 9783319220758
