
Poisson processes
Hi,
Next time I promise I won't learn a new chapter just the day before the exam :(
We have two Poisson processes $\displaystyle N_1(t)$ and $\displaystyle N_2(t)$ which are independent (with parameters $\displaystyle \lambda,\mu$)
Then $\displaystyle N(t)=N_1(t)+N_2(t)$ is a Poisson process with parameter $\displaystyle \lambda+\mu$. Okay with that.
And it follows (how ??) that $\displaystyle N_2(t)N_1(t)$ have the same distribution as $\displaystyle \sum_{i=1}^{N(t)} \epsilon_i$, where $\displaystyle P(\epsilon_i=1)=\frac{\lambda}{\lambda+\mu}$ and $\displaystyle P(\epsilon_i=1)=\frac{\mu}{\lambda+\mu}$
I don't understand at all where the last part comes from :(
Thanks for any help

If you got how the step came, please post it. I have my Random process exam tom, it will be really helpful.
Thanks in advance