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  3. problem 6 10 points assume that x and y are...

Question: problem 6 10 points assume that x and y are...

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Problem 6: 10 points Assume that X and Y are independent random variables uniformly distributed over the unit interval (0,1) 1. Define Z max (X. Y) as the larger of the two, Derive the C.DF. and density function for Z. 2. Define W min(X,Y) as the smaller of the two. Derive the C.D.F.and density function for W 3. Derive the joint density of the pair (W. Z). Specify where the density if positive and where it takes a zero value. Find the expectation for each of the variables: W. z, W2, and Z 5. Find the variance for each of the variables: W, Z, and W+Z 6. Determine the covariance between W and Z Solution
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