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

Ocean Beach, New York

... average family size is 2.91. In the village the population is spread out with 21.7% under the age of 18, 5.1% from 18 to 24, 32.6% from 25 to 44, 31.2% from 45 to 64, and ...