Question: Please show work, Thank you! PROBLEM 21.1 Suppose that two random variables X and Y have joint pdf given by firm (x,y) = 0.25(y-x) Ocx

Please show work, Thank you!

PROBLEM 21.1 Suppose that two random variables X and Y have joint pdf given by firm (x,y) = 0.25(y-x) Ocx4.6). b. Find the marginal pdf of Y. c. Use the marginal pdf of Y to determine E[Y]. PROBLEM 21.2 (pg 205, #12) X and Y: I wo components of a minicomputer have the following joint pdf for their useful lifetimes ( x.y) = xe " x20. y20 The first integral utilizes integration by pants: | u av - uv. " vau Find the marginal pdf of X (note, integration done, just evaluate limits) Note: all limits involving infinity yield zero. The marginal distribution of X has a common name. What name is given to the distribution of X and specify the one parameter value. Distribution Name: Parameter Value: C. Find the marginal pdf of Y (note, integration done, just evaluate limits) Note: all limits involving infinity yield zero. d. Are the random variables X and Y independent

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