For continuous random variables X and Y with densities p(r) and p(y) such that EX2...

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For continuous random variables X and Y with densities p(r) and p(y) such that EX2 <∞, and EY2 < x, and constants a, b E R. show a. var(aX+bY) = a²var (X) + 2abcov (X,Y) + b²var (Y). b. cov(a+bX,Y)=bcov (X.Y). c. corr(X,Y)= 0 if E(YX)=E(Y). For continuous random variables X and Y with densities p(r) and p(y) such that EX2 <∞, and EY2 < x, and constants a, b E R. show a. var(aX+bY) = a²var (X) + 2abcov (X,Y) + b²var (Y). b. cov(a+bX,Y)=bcov (X.Y). c. corr(X,Y)= 0 if E(YX)=E(Y).

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