Results 1 to 6 of 6

Math Help - Expectation of Discrete Random Variable

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    5

    Expectation of Discrete Random Variable

    Let X~Bin(n,p) be binomially distributed and define function f:R -->R by:

    a --> E(exp(aX)) . (E is the expectation)

    Find an explicit formula for f(a).

    Any hints on how to start this one? I have no idea what is going on.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    If you need to find E(e^{aX}) then isn't it just M_X(a)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2011
    Posts
    5
    Yeah, we haven't been taught moment generating functions but after reading your post I did a quick search and know what to do now. Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    Oh, in that case you just use the Expected value definition for discrete distribution
    E(e^{aX})={\Sigma}_{x}e^{ax}f_X(x) where f_X(x) is the density formula for the Binomial distribution.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2011
    Posts
    5
    Thanks, I've done that and got f(a) = (pe^a+1-p)^n .

    Now for the second part I have to show that P(X>z)\leq\frac{f(a)}{e^{az}} for a>0, z>0 .

    Any hints again?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Nov 2010
    From
    Hong Kong
    Posts
    255
    if you haven't studied inequalities yet, I don't want to spoil you all the fun ))) Just go from the first principles, ie apply the definition of P(X>z) given the distribution of X and you'll get there in no time!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Random Variable Expectation
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 5th 2010, 02:08 PM
  2. Replies: 3
    Last Post: January 13th 2010, 10:44 AM
  3. Discrete Random Variable and Expectation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 27th 2008, 12:10 PM
  4. binomial random variable Expectation
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 8th 2008, 07:39 PM
  5. Expectation of 2 Discrete Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 19th 2007, 07:00 AM

Search Tags


/mathhelpforum @mathhelpforum