I can figure out a but i cant seem to get b correct pls show

I can figure out a) but i can\'t seem to get b) correct. pls show work on how to get it right

(10 points) Suppose X and Y are independent random variables such that X N (0,1), and Y N(3,15). And, U is a linear function of the random variables X and Y 6. a) (5 points) Find E(U) E(U) = 0 b) (5 points) Find Var(U) Var(U) = 42.25

Solution

V(U) = V( 5X + XY/2)

=5²V(X) + 1/4 V(XY) + 2*5 * 1/2 * cov(X,XY)

Now, V(XY) =E(X²Y²) - E²(XY)

= E(X²)E(Y²) - E²(X)E²(Y)

= {V(X) + E²(X)} {V(Y) + E²(Y)} - 0* 9

= { 1+0} { 15 +9}

= 24

cov(X,XY) = E(X²Y) - E(X)E(XY)

= E(X²)E(Y) - 0*E(XY)

= {V(X) + E²(X)} E(Y)

= {1+0} *3

= 3

Hence V(U) = 25*1 + 24/4 + 5*3 = 46

I think the answer provided is wrong. If you have got V(U) = 46 then you are correct.