Results 1 to 6 of 6

Math Help - conditional distribution of x given x+y

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    24

    conditional distribution of x given x+y

    x,y are independent poisson RV with parameter 1 and parameter 2... determind the conditional distribution of x given x+y and find E(X|X+Y)...

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    First of all you should know the sum of two indep Poissons is another Poisson and it's mean is the sum of the other two rv's means.

    Then  P(X=a|X+Y=b) ={P(X=a,X+Y=b)\over P(X+Y=b)}={P(X=a)P(Y=b-a)\over P(X+Y=b)}

    where b\ge a. You should be able to finish this.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    24
    Thanks!
    SO, when I get the P(x=k|x+y=n)...based on the binominal property, Bin(n,p)-->E(x)=np.... (p is the parameter we get from P(x=k|x+y=n)) Am I right? Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I'll check your work, if you post it.
    Put in the poisson work and reduce it.
    Hit quote on my work above and continue with that ratio of probabilities.
    You'll learn TEX as you do the math.
    It's a win-win for you.
    Last edited by matheagle; April 7th 2009 at 02:15 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2009
    Posts
    24
    My solution:

    P(X=k|x+y=n) is bionominal distribution with BIN( n, lambda 1/ (lambda 1+lambda 2) )
    so E(x|x+y) = n* lambda 1/ (lambda 1+lambda 2)

    Am I right? Um.. I don't know where can I click "thank"? coz this is the first time I use this website.....Where is it?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I wanted you to do the math.
    I just went through those steps and yes I get a binomial with 'n' (which was my b) and parameter p={EX\over EX+EY}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint distribution, conditional distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 3rd 2011, 08:44 AM
  2. conditional distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 23rd 2011, 12:54 PM
  3. Conditional Distribution
    Posted in the Statistics Forum
    Replies: 15
    Last Post: January 26th 2011, 02:53 AM
  4. Conditional expectation of t-distribution given chi sq?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 26th 2009, 07:39 AM
  5. Conditional distribution and finding unconditional distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: December 2nd 2008, 04:48 AM

Search Tags


/mathhelpforum @mathhelpforum