A pair of random variables (X, Y) has a joint probability distribution in which the marginal distribution of X is Exp(1) and the conditional distribution of Y given X=x is Exp(x). Determine the marginal probability density function of Y. [1 mark] Determine the conditional expectation E[X|Y=y]. [1 mark]
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We know the marginal distribution of X is Exp(1), so the probability density function of X is given by: $$f_X(x) = e^{-x} \text{ for } x \geq 0$$ Show more…
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