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Math Help - Binomial with prior?

  1. #1
    Super Member Anonymous1's Avatar
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    Binomial with prior?

    Suppose X ~ Binomial(n,p) and the prior distribution for p is Beta(a,b).

    Find the mean and Variance of the marginal distribution.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I assume you want the marginal of X since the marginal of P is given (nice pun)

    E(X)=E(E(X|P))=E(nP)=nE(P)={na\over a+b}

    Next use....

    V(X)=E(V(X|P))+V(E(X|P))

    =E(nP(1-P))+V(nP)=nE(P-P^2)+n^2V(P)
    Last edited by matheagle; April 15th 2010 at 09:47 PM.
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