Encyclopedia > Moment-generating function

Article Content

Moment-generating function

In probability theory and statistics, the moment-generating function of a random variable X is

<math>M_X(t)=E\left(e^{tX}\right).</math>

The moment-generating function generates the moments of the probability distribution, as follows:

<math>E\left(X^n\right)=M_X^{(n)}(0)=\left.\frac{d^n}{dt^n}\right|_{t=0} M_X(t).</math>

Related concepts include the characteristic function and the probability-generating function.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Battle Creek, Michigan

... 16.1% have a female householder with no husband present, and 37.4% are non-families. 31.6% of all households are made up of individuals and 12.1% have someone living alone ...