Let X1, . . ., Xn be a random sample from an exponential population with parameter θ. Let Y1, . . ., Yn be the ordered random variables.
(a) Show that the sampling distributions of Y1 and Yn are given by

and

(b) Let n = 2l+1. Show that the sampling distribution of the median, M, is given by

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if y>o 0. otherwise, 72 . if y 0 otherwise 0, n!-e-m(1+1)/e[1-e-mBI. for m > 0 0, otherwise