Question: The gamma probability density function is [ f(y, r, lambda)=frac{lambda^{r}}{Gamma(r)} e^{-lambda y} y^{r-1} quad text { for } y, lambda geq 0 ] Show that

The gamma probability density function is

\[
f(y, r, \lambda)=\frac{\lambda^{r}}{\Gamma(r)} e^{-\lambda y} y^{r-1} \quad \text { for } y, \lambda \geq 0
\]

Show that the gamma is a member of the exponential family.

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