Bernoulli Distribution

The Bernoulli Distribution is defined on the domain $\{0,1\}$. It has a single parameter $\lambda \in [0,1]$ that represents the probability that $y=1$:

$$Pr(y|\lambda )=\{\begin{array}{llc}1-\lambda & & y=0\\ \lambda & & y=1\end{array}$$

This can equivalently be written as

$$Pr(y|\lambda )=(1-\lambda {)}^{1-y}\cdot {\lambda }^y$$