Let X be a random variable with moment-generating function: M(t) = 1/3+1/2*e^t+1/6*e^2t

a) Find the mean and variance of X, using the derivatives of M(t).

b) Find the pmf of X. (Hint: Use the result from question 2, and recall that the mgf of a Bernoulli(p) random variable is: M(t) = (1p)+p*e^t.)