Moment generating function and $E(2^X)$ A moment-generating function of $X$ is given by$$
M(t) = 0.3e^t + 0.4e^{2t} + 0.2e^{3t} + 0.1e^{5t}.
$$
  Find the pmf of $X$.


My solution
$$
x-f(x)\\
1-0.3\\
2-0.4\\
3-0.2\\
5-0.1\\
$$
(correct?)
The next question asks to calculate $E(2^X)$, which I am tottally unsure about. I calculated the mean as $0.22$ and variance as $5.28$.

Anyone understand what to do?
You are given the value of $M(t)=E[\mathrm e^{tX}]$ for every $t$ and you are looking for the value of $E[2^X]$. Well, note that $E[2^X]=M(t)$ for $t=$ $____$.

Sanity check: As it happens, $E[2^X]$ is an integer.
hint: $E[g(X)] = \sum g(x)P (X = x)$ Can you solve now?