Question: Need help with this problem. Let X and Y be independent, exponential random variables with mean 1/2. (a) Find M X_y(t), the moment generating function

Need help with this problem.

Let X and Y be independent, exponential random variables with mean 1/2. (a) Find M X_y(t), the moment generating function of X Y. (b) Find the joint density of U = X and V = X Y. (c) Find the marginal density of V. (d) Compute E'[X Y] using the pdf for V. (e) Compute E[X Y] using the joint pdf. (f) Compute E' [X Y] using the moment generating function found in Part (a)

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