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
BBC News 24

... subscribers could view it. In 1999, with the advent of digital television in the UK, satellite viewers were able to view the service. The BBC were initially criticized ...

 
 
 
This page was created in 33.6 ms