| Bernoulli Distribution |
|---|
If an experiment is binary having two possible outcomes, commonly called "success" and "failure," and their probabilities are respectively, θ and 1-θ, then the number of successes, 0 or 1, has a Bernoulli distribution.
A random variable X has a Bernoulli distribution and it is referred to as a Bernoulli random variable if and only if its probability distribution is given by
R has four dedicated commands for density, distribution function, quantile
function, and random generation for the Bernoulli distribution with parameter
\[
f(x; \theta ) = \theta^x \left( 1 - \theta \right)^{1-x} \qquad
\mbox{ for } \ x=0,1 .
\]
prob:
- dbern(x, prob, log = FALSE)
- pbern(q, prob, lower.tail = TRUE, log.p = FALSE)
- qbern(p, prob, lower.tail = TRUE, log.p = FALSE)
- rbern(n, prob)