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expected value question (probability)

B

bignateyk

Lifer
I am trying to figure out the mean (expected value) of the number of tries needed to successfully transmit a packet over a network.

At first I thought the obvious: its just a Bernoulli Process and can be described by a binomial random variable with mean n*p. Then I realized that this would give me the expected number of successes over a bunch of packet transmissions.

What I am looking for is the expected number of tries to successfully transmit a single packet.

It seems like it should be easy, but looking over my old probability book, I am not seeing it... anyone know the correct way? (I suck at probability)
 
nevermind... after digging around, I was able to come up with E[tries] = (1-p)sum(i * p^i)

where the sum goes from i=1 to infinity, and p = probability of packet failure.

Now, if only I could remember how to simplify a convergent infinite series...
 
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