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題組內容

(40%) If X and Y are random variabies with joint probability density function (PDF),given by

(3) (6%) Are the random variables X and Y independent? Please explain your answer.

其他申論題

(a)(8%) Determine the joint p.d.f. of z and w.

(b)(8%) Find the p.d.f. fz(x) and fw(w). Are z and w independent random variables?

(1) (6%) Piease find the marginal probability density function fx(x).

(2) (6%) Please find the mean of the random variable X.

(4) (6%) Are the random variables X and Y uncorrelated? Please expl answer.

(5) (10%) Please find the cumulative density function (CDF) of a random variable W =Y/X.

(6) (6%) Please find the PDF of the random variable W = Y/X.

(a) (10%) Find the marginal pdf of X.

(b) (10%) Find the expected value of Y.

(c) (10%) Are X and Y independent or not? Please explain your answer. (0 point if there is no explanation or if the explanation is wrong)

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