Hey guys! I am working with stochastic processes and came round the flowing problem:

$\displaystyle \tau_1,\tau_2,...\sim Exp(\lambda)$ are iid and $\displaystyle \nu$ is such independent random variable that $\displaystyle P(\nu =n)=(1-p)^{n-1},n\ge 1$. What is the distribution of $\displaystyle S_{\nu}=\tau_1+...+\tau_{\nu}$.

Well, I have tried to calculate expected value of $\displaystyle \nu$ first and then $\displaystyle S_{\nu}$ has the distribution equal to $\displaystyle Exp(\lambda )$ convolved $\displaystyle {\bf E}\nu$ times. Bot this somehow doesn't feel right. However, this looks awfully similar to compound Poison process but claim arrival times are not Poison distributed... Could anyone give a hint on this problem?