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Math Help - Marginal Probability Mass Function

  1. #1
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    Marginal Probability Mass Function

    I am having some trouble with one of my homework problems and I would like some help on the items below.


    The joint distribution of X and Y is defined by f(x,y) = |x-y|/10 for x=1,2 and y=1,2,3,4.

    a. Find f1(x), the marginal distribution of X

    This is my work so far... f1(x)=∑|x-y|/10 from y=1 to 4
    f1(x)=|x-1|/10+|x-2|/10+|x-3|/10|x-4|/10 for x=1,2
    I feel like this can be simplified but because of the absolute value I am unsure how?

    b. Find f2(y), the marginal distribution of Y

    f2(y)=∑|x-y|/10 from x=1 to 2
    f2(y)=|1-y|/10+|2-y|/10 = |3-2y|/10 for y=1,2,3,4 .....Is this correct?

    c. Find P(Y>X)
    I don't know where to start
    d. Find P(X+Y=4)
    I don't know where to start
    e. Find P(Y<=4-X)
    I don't know where to start
    f. Are X and Y independent of dependent? Why?
    Once I have the two equations for the marginal distribution of X & Y I will be able to determine independence because if f(x,y) = f1(x)f2(y) then it will be independent.


    Thanks in advance for any help you are willing to give
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  2. #2
    MHF Contributor matheagle's Avatar
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    Just fill in a table
    There are only eight possible out comes, so write vertically 1 and 2 for x
    and 1,2,3,4 horizontally for y.
    Now fill in the eight positions and go from there
    Next, obtain the marginals by summing across and down.

    The event of X+Y=4, occurs when X=2 and Y=2 OR X=1 and Y=3
    Just add the probabilities of those possible outcomes.
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