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Homework Help: Prove that you've got a probability density function

  1. Oct 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Probability of a car starting up is 0.9
    Probability of a car NOT starting up is 0.1

    Cars are tested until 2 functional cars are found.

    Find Bernoulli probability function associated and PROVE that it is a pdf (probability density function).

    2. Relevant equations


    3. The attempt at a solution

    To prove that it is a pdf, I think that I need to sum up all of the probabilities associated with the x values and show that it equals 1.

    [tex]\Sigma[/tex]x=2 to infinity p^2*(1-p)^(x-2) How do I show that this equals 1? Is it even correct?

    Keep in mind that the minimum value for the # of cars tested is 2 because we're looking for 2 functional cars, and once we've got 2, we stop the trials.
  2. jcsd
  3. Oct 7, 2009 #2


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    It isn't a PDF. You are forgetting a combinatorial factor, aren't you? If you get a second success after x trials and quit, there is more than one way that the first success could have happened. Isn't there?
    Last edited: Oct 7, 2009
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