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    Bivariate density function: Computation of Moments

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    Random variables x and y have the joint density function

    fxy(x,y)={ (a(2x+y)^2)/20 -1 < x < 1 -3 < y < 3}
    { 0 elsewhere }

    a)find the value of the constant a
    b)find all the second order moments of X and Y
    c)what are variances of X and Y
    d)what is the correlation coefficient

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    Please see the attached file.

    a) Given
    Since is a joint pdf


    Solution Summary

    A bivariate probability density function is given. The first two raw and central moments of both the variables and the correlation coefficient between them are evaluated.