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Marginal Probability function?Anyone

  1. Nov 23, 2008 #1
    Marginal Probability function????Anyone

    I have this question which I cannot seem to solve:
    The joint probability mass function p(x, y) of two discrete random variables X and Y is given by.
    p(x,y) = ([5^x][7^y][e^-5])/x!(y-x)!
    x and y are non-negative integers and x <= y
    (i) Find the marginal probability mass functions of X and Y.
     
  2. jcsd
  3. Nov 23, 2008 #2

    mathman

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    Re: Marginal Probability function????Anyone

    Sum p(x,y) over x from 0 to y to get the marginal for Y. Sum p(x,y) over y from x to oo to get the marginal for X.
     
  4. Nov 23, 2008 #3
    Re: Marginal Probability function????Anyone

    but how do we integrate the x!(y-x)!
     
  5. Nov 24, 2008 #4

    mathman

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    Re: Marginal Probability function????Anyone


    Remember we are dealing with integers, so we have to carry out summations.

    x summation to get marginal for Y: x terms are 5^x/[!(y-x)!] the sum from 0 to y can be gotten from the binomial expansion of (1+5)^y = sum 5^x[yCx], where yCx is the combinatorial symbol =y!/[x!(y-x)!].
    Put this together and you have P(Y=y) = (e^-5)(42^y)/y!
    This is wrong, since the total probability is not 1. I suggest you examine your original description.

    y summation to get marginal for X: sum from x to oo of 7^y/(y-x)!
    which is simply (7^x)(e^7).
    This leads to P(X=x) = (e^2)(35^x)/x!. This also is wrong.

    These could be corrected if e^-5 is replaced by e^-42.
     
  6. Nov 24, 2008 #5
    Re: Marginal Probability function????Anyone

    I knew something was wrong with the question:
     
    Last edited: Nov 25, 2008
  7. Nov 25, 2008 #6
    Re: Marginal Probability function????Anyone

    Thanks alot
     
  8. Nov 25, 2008 #7

    mathman

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    Re: Marginal Probability function????Anyone

    If you write it in the form p(x,y) = ([a^x][b^y][e^-c])/x!(y-x)!, you need b(a+1)=c for it to be valid.
     
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