5.5 Gamma-Poisson conjugate family 2/8

5.5.1 Poisson data model:

$Y =$ number of independent event that occur in a fixed amount of time

$$Y|y \sim Pois(\tau)$$

Probability mass function:

$$f(y|Y) = \frac{\tau^ye^-\tau}{y!} \quad for y \in \{0, 1, 2, ...\}$$

(sum to 1)

$$E(Y|\tau) = Var(Y|\tau) = \tau$$