Question: Let X and Y be random variables such that . EX = 6, . EY = 1, . Var(X) = 9, . Var(Y) = 8,

Let X and Y be random variables such that . EX = 6, . EY = 1, . Var(X) = 9, . Var(Y) = 8, and . Cov(X,Y) = 5 . Calculate the correlation of 3X+5Y and 3X + 3Y 0.9919 . First, calculate the covariance using bilinearity: Cov (aX + bY, cX + dY) = ac . Var (X) + (ad + bc) Cov (X, Y) + bd . Var (Y) . Then calculate the variances using bilinearity: Var (ax + bY) = a' Var (X) + 2ab . Cov (X, Y) + b' Var (Y) . Finally, use the formula for correlation: Correl (X, Y) = Cov( X, Y) War (X)Var( Y)

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