64. Consider the jointly discrete random variables from homework questions 54-57 with joint pmf:f(x, y) = P(X = x, Y = y) =Y =X =0121/45 6/45 3/450110/45 15/45 02 10/45 00(a) Find the covariance of X and Y.(b) Find the correlation between X and Y. For questions 54-57, consider the following experiment:A small department has 10 faculty members of whom 3 are assistant professors (aP), 5 are associateprofessors (AP), and 2 are professors (P). Of these 10 faculty members, 2 are randomly selected to beon a committee. Let X denote the number of aP selected and let Y denote the number of AP selected.X and Y are jointly discrete random variables with mass points (x, y) = {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (2,0)}.Moreover, we can find the probability associated with each of these mass points as follows:(3²)ƒ(0,0) = P(X = 0, Y = 0) = P(2 P selected) =f(0, 1) = P(X=0, Y = 1) = P(1 P, 1 AP selected)= P(X = 2, Y = 0) = P(2 aP selected)Leading to the joint pmf: f(x, y) = P(X = x, Y = y) =X = Number of aP chosen011/45 6/4510/45 f(1,1)010/45Y = Number of AP chosen 01223/4500==15(6)=1000=

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Answered: 54. Consider the jointly discrete…

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54. Consider the jointly discrete random variables from homework questions 54-57 with joint pmf: f(x, y) = P(X= x, Y = y) = X = 0 = 01/45 1 2 6/45 3/45 1 10/45 15/450 2 10/45 0 0 (a) Find the covariance of X and Y. (b) Find the correlation between X and Y.