Solved – How to prove Bernoulli distribution belongs to the exponential family

Question

According to a book, a distribution belongs to the exponential family if it can be written in the form of

I wrote the Bernoulli distribution as $\exp\Big(y \log\,[{\mu}/{(1-\mu)}] + \log\,(1-\mu)\Big)$. In this case $a(y)=y$, $b(\theta)= \log\,[{\mu}/{(1-\mu)}], c(\theta)=\log(1-\mu)$, but don't know what $d(y)$ is. Any idea what it is and why?

Answer 1

$${}{}{}{}{}d(y)=0{}{}{}{}{}$$