Bernoulli Distribution

Definition

Let $X$ be a discrete random variable with the

Parameters

• $p$: probability of success.

The random variable is said to follow a Bernoulli distribution if the probability of getting s success is described by the following

Probability Mass Function

$$\begin{array}{rrcl}{p}_X(\cdot ,p):& \{0,1\}& \to & \mathbb{R}\\ & k& \to & p^k(1-p{)}^{1-k}.\end{array}$$

Moments

• Expected value: $E[X]=p$,
• Variance: $\text{Var}(X)=p(1-p)$.

Uncertainty Estimation

Relationship with other Distributions

Binomial Distribution