I have the following Information for $x_i$ and its probabilities $p_i$:
$x_i = -1 \rightarrow p_i = 0,1$
$x_i = 0 \rightarrow p_i = 0,5$
$x_i = 2 \rightarrow p_i = 0,3$
$x_i = 3,5 \rightarrow p_i = 0,1$
I have to calculate the expectation, variance, skewness as well as the Moment generating funciton $M(t) = E[e^{tX}]$.
I've started with the expectation as follows: $E[X] = -1 \cdot 0,1+0 \cdot 0,5+2 \cdot 0,3+3,5 \cdot0,1 = 0,85$
I've continued with the usual formulas for variance and skewness. How can I calculate the mgf? Thank you!