Prove that you've got a probability density function

[pyro_peewee]

Homework Statement

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).

Homework Equations

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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.

$$\Sigma$$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.

 

[Dick]

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?