Question: Suppose that X is an exponential random variable with mean equal to 1 and that the conditional distribution of Y given X = x is

Suppose that X is an exponential random variable with mean equal to 1 and that the conditional distribution of Y given X = x is N(x, 1). (1) (5 points) Find the joint pdf of X and Y . (2) (8 points) Find the marginal pdf of Y . (3) (10 points) Find the correlation coefficient XY between X and Y

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