Suppose X and Y are random variables with EX 2 EY 3 VarX

Suppose X and Y are random variables with E(X) = 2, E(Y) = 3, Var(X) = 4, Var(Y) 10, and Cov(X, Y) =-5 Find Var(5X + 2Y) Find Cov(3X + Y, Y).

a)VAR(5X+2Y) = 5VAR(X) + 2VAR(Y)

VAR(X) = 4, VAR(Y) = 10

5*4+2*10 = 20+20 = 40

B)COV(3X+Y,Y) =

COV(3X,Y) + COV(Y,Y)

NOW COV(Y,Y) = (VAR(Y,Y) = 10

ALSO COV(X,Y) = -5

SO COV(3X,Y) = 3COV(X,Y)

= 3*-5 = -15

HENCE THE ANSWER WILL BE

-15+10 = -5