The variance of a random variable X is defined as

Var(X) = E[(X E[X])²] .

a. If E[X] = 0 and E[X²] = 1, what is the variance of X? If Y = a + bX, where a and b are constants, what is the variance of Y?

A) Var(X) = 1/2 , Var(Y) = a² + b²

B) Var(X) = 1, V ar(Y) = b²

C) Var(X) = 2, V ar(Y) = a²

D) Var(X) = 22, V ar(Y) = b²

b. Prove that Var(X) = E[X²] E[X]² . Please show your work in detail