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)

\[E(Y|\tau) = Var(Y|\tau) = \tau \]