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Probability, please help

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Problem H-10. We will compute the mean of the geometric distribution. (Note: It's also possible to
    compute E(X^2) and then Var(X) = E(X^2)−(E(X))^2 by steps similar to these.)

    (a) Show that
    E(X) = (k=1 to infinity summation symbol) (k *q^k−1* p)
    where q = 1−p.

    (b) Show that the above summation can be rewritten as follows:
    E(X) = p* d/dq (k=1 to infinity summation symbol) q^k

    (c) The sum in part (b) is a geometric series. Evaluate the geometric series; replace the sum in (b) by this value; and do the derivative d/dq. The final answer will be a quotient of polynomials involving p
    and q; there will not be an in nite sum remaining.

    (d) Plug in q = 1−p and simplify to get the final answer.
     
  2. jcsd
  3. Feb 23, 2012 #2

    kai_sikorski

    User Avatar
    Gold Member

    hi shawn,

    Welcome to the forums.

    You need to show an attempt at a solution before we can help you.
     
  4. Feb 23, 2012 #3
    kinda how no clue how to go about it let me think about it a little more and get back
     
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