Moment-generating function 动差生成函数
（重定向自Moment generating function）
In probability theory and statistics, the moment-generating function of a random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables. Note, however, that not all random variables have moment-generating functions.
![M_X(t)=E\left(e^{tX}\right), \quad t \in \mathbb{R}](/Images/godic/202501/28/9653400d9d07eb522bbc14bd90025a690758.png")