Question

The moment generating function for the discrete random variable is given by ________
Fill in the blank.

Answer 1

Concept :- moment generating function $M_X(t)$ of X is $E(e^{tX})${ by definition } by the usual formula for the expectation ,
$M_X(t)= E(e^{tX})=\sum_{k=1}^n \frac{1}{n}e^{tx_k}$

Hence, the moment generating function for the discrete random variable is given by $M_X(t)= E(e^{tX})=\sum_{k=1}^n \frac{1}{n}e^{tx_k}$