Assignment. Let W= (X, Y, 2) be jointly discrete random vector. Construct a valid joint pmf of W (with at least 12 possible mass points) and derive all marginal prifs and joint pofs of and present using tables. subvector
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- An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. y p(x, y) 0 5 10 15 x 0 0.01 0.06 0.02 0.10 5 0.04 0.16 0.20 0.10 10 0.01 0.15 0.14 0.01 (a) Compute the covariance for X and Y. (Round your answer to two decimal places.)Cov(X, Y) = (b) Compute ρ for X and Y. (Round your answer to two decimal places.)ρ =Let X = (X₁, . . . , Xn) denote an (n × 1) vector of independent random variables Xi∼ N (0, 1), i = 1, . . . , n. Let A = [aij] denote an (m × n) matrix, and define a random vector Y = (Y₁, . .. , Ym) asY = AX. Show that Cov(Yi, Yj) Which of the following lines is a valid argument? See attached picAn instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. y p(x, y) 0 5 10 15 x 0.01 0.06 0.02 0.10 5 0.04 0.16 0.20 0.10 10 0.01 0.15 0.14 0.01 (a) Compute the covariance for X and Y. (Round your answer to two decimal places.)Cov(X, Y) = (b) Compute ? for X and Y. (Round your answer to two decimal places.)? =