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