Bernoulli Distribution

Definition

A simple probability distribution for anything with success or failure- like flipping a coin. It's a discrete probability distribution with only two outcomes. Success or Failure.

Properties

1. Mean: $p$
2. Variance: $p(1-p)$

Relationship

1. It's a special case of the Binomial Distribution when there is only one event! For example, if $n$ (number of events) and $k$ (number of subset) are equal to 1 :

which then reduces down to:

Trivial! So

2. The Geometric distribution models the number of i.i.d Bernoulli trials to get a success.

References