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Probability and Voting

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data
    In a town there are r+1 Republicans and d+1 Democrats. There is a Republican candidate and a Democratic candidate, both of whom will vote for themselves. Aside from them, a Republican voter will vote for a Democrat with probability pRD and a Democrat will vote for a Republican with probability pDR. Assume the voters behave independently.
    What is the covariance of the number of votes the Republican receives and the number of votes the Democrat receives?

    2. Relevant equations
    Cov(X,Y) = E(XY) - E(X)E(Y)

    3. The attempt at a solution
    I let X=votes for Republican, Y=votes for Democrat.
    I got that E(X)=1+d*pDR + r(1-pRD) and
    E(Y) = 1+r*pRD + d(1-pDR)
    But how do you get E(XY). I was thinking of representing X as a sum of Bernoulli's (1 if the vote is for the Republican, 0 if for the Democrat), but I still don't see how I would get E(XY) with that approach.

  2. jcsd
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