Finding the Optimal Distribution for Successive Trials

[ArcanaNoir]

Homework Statement

The probability of an experiment is p. Show that the expected number of trials for two successes in a row is $\frac{p+1}{p^2}$

I just don't know what distribution to work with here.

 

[canis89]

Hi, this kind problem has been examined very thoroughly by Mike Spivey at

http://math.stackexchange.com/quest...n-a-row-at-the-k-th-bernoulli-trial-geometric

The discussion covers the derivation of the distribution's pmf and PGF.

 

[ArcanaNoir]

Thank you very much :)