Discrete random variable

Bernoulli trial

A Bernoulli trial is an experiment with two possible outcomes, namely success and failure. prob For any event in a probability model has an associated Bernoulli random variable called its indicator random variable¹, where

We say where . The sum of repeated independent but identical Bernoulli trials follows a Binomial distribution.

Properties

Let and

1. Expectation:
2. Variance:
3. Moment-generating function:
4. Probability-generating function:

We have the further properties

1. for any

Indicator random variables

Let in a probability model

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Footnotes

1. This is a special case of an indicator function. ↩