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題組內容

(17%) Random variables X and Y have joint probability density function
Let A =.

(b) (4%) Find(x, y).

其他申論題

(a) (3%) Find the marginal probability distribution function of Y, i.e. fy (y).

(b) (3%) Find the mean of Y.

(c) (4%) Find the variance of Y.

(a) (4%) Find fx(x).

(d) (5%) Find E[Y|A].

(a) (4%) Find the constant C.

(b) (4%) Find the conditional probability density function .

(c) (8%) Let U = X + 2Y and V = X -Y. What is the correlation coeficient of U and V?

(d) (8%) Let Z = 3X + 2Y. Derive the moment generating function . You have to give the derivation, not just the an- swer.

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