Question: Let X be a random variable having density given by f(x; , ) = ( a / (x+) +1 if x > 0, 0 elsewhere,

Let X be a random variable having density given by f(x; , ) = ( a / (x+)+1 if x > 0, 0 elsewhere, where > 0 and > 0 are parameters.

(a) If > 0, show that E [X] = / 1 .

(b) Let k N such that > k. If X has pdf f(x; , ) and Y has pdf f(y; 1, ), where f is as above, show that E[Xk] = (k / 1) E[Yk - 1] .

(c) Deduce a general formula for E[Xk] when > k

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