can anyone help me to inform the name of any book where I can get the following theorem, or give some detailed hint to solve this one:
Let $X$ and $Y$ be two random variables, if the moment generating functions of $X$ and $Y$ are equal then the probability distributions of $X$ and $Y$ will be same. In other words, if $E(e^{tX})=E(e^{tY})$ for all $t$ real, then $X$ and $Y$ have the same distribution.