Question: 20. Let W be a gamma random variable with parameters (r, B), and suppose that conditional on W = w, X1, X2, , X, are

20. Let W be a gamma random variable with parameters (r, B), and suppose that conditional on W = w, X1, X2, …, X, are independent exponential random variables with rate w. Show that the conditional distribution of W given that X₁ = x1, X2 = x2,..., X, = x, is gamma with parameters

(r + n, B + Σ x,)

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