Question: Suppose X Uniform(1, 2) and given X = x, Y is an exponential random variable with parameter = x, so we can write

Suppose X ∼ Uniform(1, 2) and given X = x, Y is an exponential random variable with parameter λ = x, so we can write Y |X = x ∼ Exponential(x).

We sometimes write this as Y |X ∼ Exponential(X).

a. Find EY.

b. Find V ar(Y).

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