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題組內容

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

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

其他申論題

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

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

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

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

(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)

8.(10%) The joint p.d.f. of x and y is for some k. Deter-mine the conditional p.d.f..

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

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