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    Transformations - Joint and Marginal Probability Mass Function

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    Let X1 and X2 have the joint pmf p(x1,x2) = (x1x2)/36 x1=1,2,3 and x2=1,2,3, zero elsewhere. Find first the joint pmf of Y1=X1X2 and Y2=X2, and then find the marginal pmf of Y1.

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    Solution Preview

    See the attachment please.

    Let X1 and X2 have the joint pmf p(x1,x2) = (x1x2)/36 x1=1,2,3 and x2=1,2,3, zero elsewhere. Find first the joint pmf of Y1=X1X2 and Y2=X2, and then find the marginal pmf of Y1.

    Solution.
    By given information, we have

    -------------------------------------------------------------------------------------------------------------------
    X1 1 2 3
    X2
    1 1/36 2/36 3/36

    2 2/36 ...

    Solution Summary

    This solution is provided in 184 words. It uses a chart and step-by-step equations to find the marginal and joint pdf.

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