Bernoulli random variable

Short description and context

Bernoulli random variable

The Bernoulli random variable is a discrete random variable that is often used to model experiments that have only two outcomes. These types of experiments are sometimes called trials. The probability mass function for the Bernoulli random variable is: $$ f_X(x) = P(X=x) = \begin{cases} 1-p & \textrm{if} \quad x=0 \\ p & \textrm{if} \quad x=1 \\ 0 & \textrm{otherwise} \end{cases} $$ The expectation for a Bernoulli random variable, $X$, is $\mathbb{E}(X) = p$ and the variance is $\textrm{var}(X) = p(1-p)$.

Syllabus Aims

  • You should be able to explain what types of phenomena can be modelled using the Bernoulli random variable.
  • You should be able to write out the probability mass function for the Bernoulli random variable.
  • You should be able to sketch the probability distribution function for this random variable.
  • You should be able to prove that the probability mass function for the Bernoulli random variable is properly normalized.
  • You should be able to derive expressions for the expectation and variance of this random variable.

Extending your understanding

Description and link

Module

Author

EXAMPLE: project on bernoulli random variables SOR3012 G. Tribello

Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite