Bernoulli Distribution

Gist

A simple probability distribution for anything with success or failure- like flipping a coin.

Definiton

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.

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

References