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Math Help - marginal pmfs

  1. #1
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    marginal pmfs

    The joint p.m.f. of X and Y is f(x,y)=1/6, 0 \le x+y \le2, where x and y are integers.

    a) sketch the support of x and y.

    (0,0),(0,1),(0,2),(1,0),(1,1),(2,0)

    b) record the marginal pmfs of f_{1}(x) and f_{2}(y) in the margins

    f_{1}(0)=1/6+1/6+1/6=1/3
    f_{1}(1)=1/6+1/6=1/3<br />
    f_{1}(2)=1/6
    f_{2}(0)=1/2
    f_{2}(1)=1/3
    f_{2}(2)=1/6

    c) compute cov(x,y)

    mean[(x-mean(x))*(y-mean(y)]=1/6[(0-2/3)(0-2/3)+(0-2/3)(1-2/3)+(0-2/3)(2-2/3)+(1-2/3)(0-2/3)+(1-2/3)(1-2/3)+(2-2/3)(0-2/3)]=1/6[-15/9]=-5/18

    d) Determine the correlation coefficient

    =\frac{-5/18}{\sqrt{5}/3*\sqrt{5}/3}=-1/2

    e) Find the best fitting line.

    I am hoping my other answers are correct, but I don't know what they mean for this one. Thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    The best way to obtain the covariance is by E(XY)-E(X)E(Y), since here x and y are zero quite often.

    In fact E(XY)=1/6 since the only time you don't have a zero is when x=y=1.
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