User:IssaRice/Gamma distribution

https://www.youtube.com/watch?v=Qjeswpm0cWY

ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n things happen, and this will be the sum $T_n=\sum _{j=1}^n{X}_j$, where each $X_j\sim \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}(\lambda )$. Now this sum happens to have distribution $\mathrm{G}\mathrm{a}\mathrm{m}\mathrm{m}\mathrm{a}(n,\lambda )$.