Prove that E[(Z - Uz)^2] = c^2(E[X^2] - (Ux)^2) if X is a discrete random variable and b and c are constants and define a new random variable Z = b + cX
Note : Uz = mu of z = mean of z
Ux = mu of x = mean of x
E ((Z-Uz)^2) = E(Z^2) - Uz^2 --- Eq1
Uz = cUx
subbing in z = b + cX in Eq1
=E(b^2 + 2cX + (cX)^2) - (cUx)^2
= b^2 + 2c *(E(X)) + c^2(E(X^2)) - c^2 * Ux^2
= b^2 + 2cE(X) + c^2((E(X^2)) - Ux^2)
Why do i get b^2 + 2cE(X) extra???????