Problem regarding the exponential random variable

Reference no: EM13985311

1. Show that an exponential random variable such that the inverse of the parameter is gamma-distributed is Pareto-distributed. More precisely, show that if X | M = m ∈ Exp(m) with M-1 ∈ Γ(p, a), then X has a (translated) Pareto distribution.

2. Let X and Y be random variables such that Y | X = x ∈ Exp(1/x) with X ∈ Γ(2, 1).

(a) Show that Y has a translated Pareto distribution.

(b) Compute E Y .

Reference no: EM13985311

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