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Unformatted text preview: 0.0 0.0 5 1 12 32 31 19 21 0.3 0.2 0.1 0.0 0.0 0.0 (a) Plot the marginal PMF of the two indices. (b) Plot the conditional PMFs of (X|Y = 8) and (X|Y = 6). (c) Plot the conditional PMF of (Y|X 50). (d) What is the probability that an applicant with Y = 7 is accepted. (e) Are X and Y independent? Why? Problem 3 In Bounty Town, U.S.A., total precipitation during the crop-growing season, Q, has a uniform distribution between 2 and 4 inches. The total crop value $ depends on Q in such a way that ($|Q = q) has uniform distribution (in millions of dollars) between (2q 1) and (2q + 1). Note that the possible values of (Q,$) are inside the parallelepiped shaded in the figure below: 2q + 1 $ 2q - 1 2 4 q (a) What is the joint PDF of Q and $? (b) What is the marginal PDF of $? (c) What value of $ is exceeded on average every 5 years? Read Application Examples 7, 9 and 10. ....
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- Spring '05