The Bernoulli distribution is a discrete probability distribution that describes the probability of a binary outcome (such as success or failure). It is named after Jacob Bernoulli, a Swiss mathematician.

Bernoulli Trial

A Bernoulli trial is a statistical experiment with only two possible outcomes: success or failure.

Bernoulli trials are often used to model the outcome of a single event or experiment where the probability of success is known. For example, flipping a coin, since there are only two possible outcomes.

The probability of success in a Bernoulli trial is denoted by the letter "p", and the probability of failure is denoted by the letter "q" (where q = 1 - p). For example, if the probability of flipping heads in a coin flip is 0.5, then the probability of flipping tails is 0.5 (since 1 - 0.5 = 0.5).

The Bernoulli distribution is a probability distribution that describes the outcomes of a series of Bernoulli trials.

Bernoulli Distribution

The Bernoulli distribution is defined by a single parameter: the probability of success (p). This parameter represents the probability that the outcome will be "success," with the probability of failure being 1 - p.

Properties of the Bernoulli Distribution:

The Bernoulli distribution has several important properties, including:

• Discrete values: The Bernoulli distribution is a discrete probability distribution, meaning that it can take only a finite number of values (either 0 or 1).
• Binary outcomes: The Bernoulli distribution describes the probability of a binary outcome, such as success or failure.
• A special case of Binomial Distribution: The Bernoulli distribution is a special case of the binomial distribution when there is only one trial being conducted.