Results 1 to 2 of 2

Math Help - Poisson Distribution

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    17

    Poisson Distribution

    Let X be the poisson random variable with parameter lambda. Obtain E(X^3) and E(X^4).

    Please explain to me for the E(X^3) and i'll do the other one by myself.
    Thank you loads
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    You can compute the moment generating function :

    M_X(t)=E[e^{tX}]=\sum_{k=0}^\infty e^{tk}\cdot\frac{e^{-\lambda}\lambda^k}{k!}=e^{-\lambda}\sum_{k=0}^\infty \frac{(e^t\lambda)^k}{k!}=e^{-\lambda}e^{\lambda e^t}=e^{\lambda(e^t-1)}

    And use this property : E[X^n]=\left. M_X^{(n)}(t)\right|_{t=0} (n-th derivative at t=0)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 27th 2011, 02:08 PM
  2. Poisson distribution and asymptotic normal distribution.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 18th 2010, 06:52 AM
  3. Poisson Distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 10th 2009, 01:02 AM
  4. Poisson Distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 8th 2009, 11:02 AM
  5. Poisson Distribution HELP!!!
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 7th 2009, 05:06 AM

Search Tags


/mathhelpforum @mathhelpforum