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Math Help - joint Probability mass function

  1. #1
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    joint Probability mass function

    if the joint PMF is p(x,y)=k(x+y)

    find the PMF 3X-2Y

    is this given by substituting x=3X
    y=-2Y
    in which case it becomes:
    p(3x,-2y)=k(9x+4y)
    i am not sure if this is correct:
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  2. #2
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    Your answer is not correct. You can see that is wrong by trying to use it to answer the question "what is the probability that 3x-2y = 5". There is no way to input this information into your function to get an answer.

    Starting over, define a single variable Z = 3X - 2Y

    You want the PMF of Z

    P(Z=z) = P(3X - 2Y = z) = P(Y=\frac{z+3X}{2})

    ie, to get a particular value of Z we cna have any value of X, provided that Y = (z+3x}/2

    P(Z=z) = \sum_x k \left[ x^2 + \left( \frac{z+3x}{2} \right)^2 \right]

    The last step is called the method of convolutions, which hopefully you have seen before if you were set this problem.
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  3. #3
    MHF Contributor matheagle's Avatar
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    I don't even know if the underlying joint distribution is discrete or continuous.
    Nor do I know the support.
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