What is a Bernoulli Distribution?
Bernoulli distribution is an independent probability function where a random variable can have only two possible values: either 1 for success or 0 for failure. This is similar to binomial distribution, but for a single yes/no test known as “Bernoulli trials.” Success and failure are measured relative to the expected or predicted outcome of any probability model.
- Binomial distribution
- Geometric distribution
- Negative binomial distribution
Independence in Bernoulli Distribution
A key aspect of every Bernoulli trial is that each action must be independent of the previous event. No matter how often the event is repeated, the probabilities must remain the same across all trials.
For example, winning a raffle contest is an independent event. The odds of winning on any single ticket are the same as winning by purchasing any other ticket. Of course, drawing raffle numbers is a dependent event. The ticket numbers aren’t replaced, so the probability of picking successive numbers depends upon how many balls are left. While those probabilities can be modeled with other distribution methods, they don’t conform to Bernoulli trials since the events of picking raffle numbers are connected to each other.