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Unformatted text preview: | X | ,-| Y | ). ( d ) Find Var(4 X-3 Y ). Problem 4 Let X be a random variable with a pdf f X ( x ) = ± 1 if 0 ≤ x ≤ 1 0 otherwise . Let Y = X 3 . Compute Cov( X,Y ). Problem 5 A fair coin is tossed n times. Every time is shows a head (and only in that case), a fair die is rolled and its result recorded. Let X be the sum of all the results of the rolls of the die. Find the mean and the variance of X . Problem 6 A committee of three persons is to be randomly selected from a group consisting of 2 Republicans, 3 Democrats and four Inde-pendents. Let X denote the number of Republicans and Y the number of Democrats on the committee. 1 ( a ) Find Cov( X,Y ). ( b ) Find Var( X + Y ) ﬁrst by computing the pmf of X + Y and then by using your computations in part ( a ) and the formula for the variance of a sum. Did you get the same answer? Due:October 13, at 4 p.m. 2...
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- Variance, Probability distribution, Probability theory, Cov