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Probability - Bernoulli stuff

  1. Nov 3, 2006 #1


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    Consider a sequence of Bernoulli trials where we play until the rth success is attained. Denote [itex]\Omega[/itex] the fundamental set.

    We define a function P on [itex]\Omega[/itex] by saying say that an elementary event that is a k-tuple has a probability of occurence of


    because the trials are independant and the probability of success at each of them is p and the probability of failure is q.

    Now I ask wheter or not with these probabilities assigned to each elementary event, we do have [itex]P(\Omega)=1[/itex]? Did I miss something and it is implied that [itex]P(\Omega)=1[/itex], or we have to show that


    to show that P defined above is indeed a probability on [itex]\Omega[/itex]?
    Last edited: Nov 3, 2006
  2. jcsd
  3. Nov 6, 2006 #2
    that looks like a negative binomial distribution... not sure. but you should probably prove it sums to 1.
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