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Binomial Distribution

  1. Jul 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose that the conditional distribution of X given that N = n is binomial (n, 1/2) and the distribution of N is uniform over {2,4,6}

    a) Determine P(X=2, N = 4)
    b) Determine P(X=1)
    c) Determine P(N = 4| X =1)

    2. Relevant equations



    3. The attempt at a solution

    the way I understood the question was that X|N~bin(n, 1/2)

    for a) I did (4C2)(0.5)2(0.5)2 = 0.375

    I'm stuck for b). Any hints?
     
  2. jcsd
  3. Jul 25, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that is correct.

    Since N is uniform on 2, 4, 6, find P(X|N=2), P(X|N= 4), and P(X|N= 6). P(N= 2)= P(N= 4)= P(N= 6)= 1/3.
     
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