For each of the following random variables: find moment generating function, $\mu'_1$, $\mu'_2$, $\mu'_3$,
variance, and standard deviation. Note: find moments using moment generating function.
1. R(X) = {1, 2, 3, ...}, $p_X(1) = \frac{1}{4}$, $p_X(2) = \frac{3}{4^2}$, $p_X(3) = \frac{3^2}{4^3}$, ..., $p_X(k) = \frac{3^{k-1}}{4^k}$.
2. R(Y) = {0, 1, 2, ..., 100}, $p_Y(k) = \frac{100!}{k!(100-k)!} \cdot \frac{2^k}{3^{100}}$.
3. R(Z) = {0, 1, 2, 3, ...}, $p_Z(k) = \frac{2^k}{k!}e^{-2}$.