Random Variableshard
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Let XX and YY be two random variables such that E[X]=2E[X] = 2, Var(X)=4Var(X) = 4, E[Y]=5E[Y] = 5, and Var(Y)=9Var(Y) = 9. The correlation between XX and YY is given by ρ(X,Y)=0.25\rho(X, Y) = 0.25. Calculate the variance of the random variable Z=3X4Y+12Z = 3X - 4Y + 12.