Let $X$ be a random variable with probability mass function $P (X = 1) = , P (X = 2) =$. Provide answers to the following to two decimal places where appropriate.

Part a) Find $Var(X)$.


Part b) Find $E(^X)$.


Part c) Which of the following is the moment generating function (MGF) $M_X(t)$ of $X$?

A. $e^t - e^{2t}$
B. $e^{2t} - e^t$
C. $( )e^{3t}$
D. $+ e^t$
E. $e^t + e^{2t}$
F. $+ e^t$


Part d) Evaluate the MGF $M_X(t)$ at the point $t =$.