Let h(x) = P{ T i=1 Xi > x} where X1, X2,... are independent random variables having distribution function Fe and T is independent of

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Let h(x) = P{

T i=1 Xi > x} where X1, X2,... are independent random variables having distribution function Fe and T is independent of the Xi and has probability mass function P{T = n} = ρn(1 − ρ), n 0. Show that h(x)

satisfies Equation (7.53).

Hint: Start by conditioning on whether T = 0 or T > 0.