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Marginal Probability

  1. Feb 17, 2008 #1
    Find the marginal probability functions of a) X and b) Y
    f(x,y)=cxy for x=1,2,3 y=1,2,3 (discrete data)

    The first thing I did was solve for c, which turned out to be 1/36. The book confirmed this.

    Next I setup a table, for x=1 the total would be 6c, x=2 12c, x=3 18c.

    So for the marginal probability for X, where x=1 I took 6 (1/36) 1/6, x=2 12(1/36)=1/3, & finally x=3 18(1/36)=1/2

    so the marginal probability for X is as follows
    f(x)= 1/6 for x=1
    1/3 for x=2
    1/2 for x=3

    However, this is what the book has for an answer
    f(x)= x/6 for x=1,2,3

    So I'm kinda confused here. The book has a similar example & I did this problem exactly like the example, so where am I going wrong?
     
  2. jcsd
  3. Feb 17, 2008 #2
    The book is correct. You need to sum over y.

    [tex]f_X(x)=\sum_{y=1}^3f_{X,Y}(x,y)=\sum_{y=1}^3\frac{1}{36}xy=\frac{1}{36}x(1+2+3)=\frac{x}{6}[/tex]

    Edit: I just noticed that you do have the correct answer. Think about it.
     
    Last edited: Feb 17, 2008
  4. Feb 17, 2008 #3
    Indeed, you are correct... :)
     
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