Distributionshard
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Let XN(1,4)X \sim N(1, 4) and YN(2,9)Y \sim N(2, 9) be independent normal random variables. Define U=2X+3YU = 2X + 3Y and V=3X2YV = 3X - 2Y. What is the covariance Cov(U,V)Cov(U, V)?