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Negative binomial distribution

  1. Dec 31, 2013 #1
    1. The problem statement, all variables and given/known data

    Repeatdly roll a fair die until the outcome 3 has accurred on the 4th roll. Let
    X be the number of times needed in order to achieve this goal. Find E(X)
    and Var(X)

    2. Relevant equations

    3. The attempt at a solution

    I am having trouble deciphering this question. Is the first sentence saying to roll a die until you get a 3 on the fourth roll? thus the event of a success is when you get a 3 on the fourth roll? but what is number of successes? which you need to know in order to find the mean in a negative binomial distribution.

    Apparently E(X) = 24.
  2. jcsd
  3. Dec 31, 2013 #2

    Ray Vickson

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    Homework Helper

    Please clarify: do you mean the first 1, 2 or 3 tosses could also result in a "3", and that you look only at the result of the fourth toss? Or, do you mean that you count the rolls only if the first three are non-3s and the fourth is a 3? It makes a huge difference!
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