A) What is a Bernoulli trial and a Bernoulli distribution?

Bernoulli#discrete

A Bernoulli trial is a random experiment (e.g., a coin toss) in which a dichotomy is observed (e.g., only heads or tails).

The Bernoulli distribution models the outcome of a single Bernoulli trial. Its PMF is: [ P(X=1) = p ] [ P(X=0) = 1-p ] Where:

  • ( p ) is the probability of success (e.g., getting heads).
  • Expected value (mean) = ( p )
  • Variance = ( p(1-p) )

Special Facts

  • Describes the distribution of the indicator random variable