i) For a random variable X, suppose that E[X]=4and Var(X)=5. Then

(a) E[(5+X)²]=

(b) Var(4+6X)=

ii) A 4-sided die is rolled twice. Let X be thesum of the two rolls, Y be the first minus the second, and Z be the2 times the first, minus the second.

(a) Compute Cov(X,Y):Cov(X,Y)=

(b) Compute Cov(X,Z):Cov(X,Z)=

iii)

(1 point) Let X and Y be random variables with joint density function f(x, y) = { f S4e-4x/x, 0, Compute Cov(X, Y). Cov(X, Y) = 0x < ,0 y x otherwise.