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
Westhampton Beach, New York

... living together, 11.1% have a female householder with no husband present, and 38.1% are non-families. 32.7% of all households are made up of individuals and 13.7% ...

 
 
 
This page was created in 30.7 ms