Given Ex and Vx 2 and y 2x 3 then which of the following

Given E(x) = and V(x) = 2 and y = 2x + 3, then which of the following is true about E(y) and V(y)

A) E(y) = 2 + 3 and V(y) = 42

B) E(y) = 2 + 3 and V(y) = 42 + 9

C) E(y) = 2 and V(y) = 42 + 3

D) E(y) = 2 and V(y) = 42

Solution

Sol)

E(x) = and V(x) = ²

y = 2x + 3

Apply Expectation on both side

E(y) = E(2x + 3)

E(y) = E(2x) +E(3)

E(y) = 2 E(x) +3

E(y) = 2 +3

Now

y = 2x + 3

apply variance on both sides

V(y) = V(2x + 3)

V(y) = V(2x) + V(3)

V(y) = 4 V(x) + 0

V(y)= 4 ²

Hence Option A is correct