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    Probability and conditional distributions

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    Probability and conditional distributions. See attached file for full problem description.

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    Please see the attached file.

    I think you know the basic integration steps. So I am avoiding the integration steps
    9. a. Given , 0 < x < y , 0 < y <1
    The given range can be combined and written in the form 0 < x < y < 1.
    To find the marginal density of X (or Y) , integrate f (x,y) w.r.t Y (or X). (Note that range of integration should be taken from the combined range whenever x and y simultaneously included in the integration)
    The marginal densities is given by,

    = 2 (1-x) , 0 < x < 1

    = 2y , 0 < y < 1
    The ...

    Solution Summary

    Solution reveals some relationships between the binomial and Poisson distribution. Also it includes method for finding the correlation coefficient between two random variables