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Math Help - Another jpoint distribution problem

  1. #1
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    Another jpoint distribution problem

    Quote Originally Posted by braddy

    problem 2:
    A traffic engineer is studying the number of vehicles that arrive, during a certain 2-minute period, at two streets corners that are close to each other. Let X be the number of vehicles at on street corner and Y the number at the other. The enginner knows the joint distribution probability distribution of X and Y is:
    -f(x,y)=(9/16)*(1/4)^(x+y), x=0,1,2,3..., y=0,1,2,....
    - 0 elsewhere

    For example P(X=1,Y=1)=0.035.
    The enginner calculated E(X)=E(Y)=1/3, and Var(X)=Var(Y)=4/9.
    He has calculated that X and Y are independent.
    I'm not sure what is being asked here. The X and Y are independent
    can be deduced form:

    f(x,y)= g(x)g(y), x=0,1,.. y=0,1, ..

    where g(x)=(3/4)(1/4)^x since g(x) is a probability distribution, and as
    the joint distribution is the product of marginal distributions for X and Y,
    X and Y are independent.

    1-Find rho, the correlation coefficient of X and Y.
    From the book, I get the formula
    rho=E(((X-mean1)/var1)*((X-mean2)/var2))
    but when I tried to compute it, I get undefined.
    rho= sum_{x=1 to infty, y=1 to infty} (x-xbar)(y-ybar)/sqrt(var(x)var(y)) f(x,y)

    but this sum is seperable to:

    rho= [sum_{x=1 to infty} (x-xbar)/sqrt(var(x)) g(x)][sum_{y=1 to infty} (y-ybar)/sqrt(var(y)) g(y)] = 0

    RonL
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    OK thanks
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