Suppose X and Y are independent random variables with Exp(θ = 2) distribution. Note that, we...

Suppose X and Y are independent random variables with Exp(θ = 2) distribution. Note that, we say X ∼ Exp(θ) if its pdf is f(x) = 1/θ e^(−x/θ) , for x > 0 and θ > 0.

(a) What is the joint probability density function (pdf) of (X, Y )?

(b) Use the change of variable technique (transformation technique) to evaluate the joint pdf fW,Z (w, z) of (W, Z), where W = X −Y and Z = Y . Also, find the region (support) where fW,Z (w, z) is positive.

(c) Show that the marginal pdf of W is fW (w) = 1/4e^−|w|/2 for − ∞ < w < ∞.

Expert Solution

orchestra answered 2 years ago

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Suppose X and Y are independent random variables with Exp(θ = 2) distribution. Note that, we...

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