Bernoulli Distribution - rFronteddu/general_wiki GitHub Wiki

bernoulli

  • X ~ Bern(p): "Variable SX follows a Bernoulli distribution with a probability of success equal to p."
  • Describes events with 1 trial and 2 possible outcomes (ex. coin flip, single F/T question)
  • When we use Bern, p is known or we have past data indicating some experimental probability.
  • Conventionally, p is the highest probability, and 1 - p is the other. Moreover, we assign values 1 to p and 0 to 1 - p. That way E(X) expresses the likelihood of the favored event.
    • E(X) = 1 * p + 0 * (1 - p) = p
  • $σ^2={(x_0 - μ)}^2 * P(x_0) + {(x_1 - μ)}^2 * P(x_1) = p(1 - p)$
  • since $x_0$ = 0, μ = p, $P(x_0) = 1-p$ and $P(x_1)$ = p
    • The variance and mean are not particularly informative.
    • Note that this distribution models only single-trial experiments. For multiple trials, use Binomial distribution.