5.7 Gamma-Poisson conjugate family 4/8

5.7.1 Joint probability mass function

We have pmf for each day but if we want for $n$ day we need to use joint probably mass function. (product of every pmf)

$$L(\tau|\overrightarrow{y}) = \frac{\tau^{\sum y_i e^{-n\tau}}}{\prod_{i=n}^{n} y!} \propto e^{-n\tau} \tau^{\sum y_i}$$

We just need : $n$ and $\sum y_i$