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Math Help - [SOLVED] Binomial Geometric

  1. #1
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    [SOLVED] Binomial Geometric

    A= X B(3,1/6)
    B= X Geo (1/2)


    Find

    i) P(B>2)
    ii) P(A=B)


    thanks
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  2. #2
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    Quote Originally Posted by gracey View Post
    A= X B(3,1/6)
    B= X Geo (1/2)


    Find

    i) P(B>2)
    ii) P(A=B)


    thanks
    Do you mean that A is a random variable that has a binomial distribution with n = 3 and p = 1/6?

    Do oyu mean that B is a random variable that has a geometric distribution with p = 1/2?

    If so, then:

    i) Two options:

    1. \Pr(B > 2) = 1 - \Pr(B = 1) - \Pr(B = 2) = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}.

    2. From the cdf, \Pr(B > 2) = 1 - \Pr(B \leq 2) = 1 - \left[1 - \left(1 - \frac{1}{2}\right)^2\right] = \left(\frac{1}{2}\right)^2 = \frac{1}{4}.


    ii) Pr(A = B) = Pr(A = 1 | B = 1) Pr(B = 1) + Pr(A = 2 | B = 2) Pr(B = 2) + Pr(A = 3 | B = 3) Pr(B = 3)

    Assuming A and B are independent:

    = Pr(A = 1) Pr(B = 1) + Pr(A = 2) Pr(B = 2) + Pr(A = 3) Pr(B = 3)

    = \left[ 3 \left(\frac{1}{6}\right) \left(\frac{5}{6}\right)^2 \right] \left(\frac{1}{2}\right) + \left[ 3 \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right) \right] \left(\frac{1}{2}\right)^2 + \left[\left(\frac{1}{6}\right)^3 \right] \left(\frac{1}{2}\right)^3 = .....
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  3. #3
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    thankyou that is excellent
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