Chapter 2.4, Problem 19E

Define the pmf and give the values of $\mu ,{\sigma }^2$, and $\sigma$ when the moment-generating function of X is defined by

(a) $M\left(t\right)=\frac{1}{3}+\left(\frac{2}{3}\right)e^t$.

(b) $M\left(t\right)={\left(0.25+0.75e^t\right)}^{12}$.