Suppose Y 2X 3 Also suppose that EY 9 and EY2 100 Find E

Suppose Y = 2X + 3. Also, suppose that EY = 9 and EY^2 = 100. Find E(X) and Var(X).

E(2X+3) = 9

2E(X) +3= 9 Therefore E(X) = 6/2 = 3

E(4X^2+12X+9) = 100

or,

4E(X^2)+12E(X)+9 = 100

4E(X^2)+45=100

E(X^2) = 13.75

Var(X) = E(X^2) - (E(X))^2

=13.75-9 = 4.75