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Bernoulli Distribution

Bernoulli distribution is a statistical distribution named after Swiss mathematician, Jacob Bernoulli.

It is a discrete probability distribution used for a series of Bernoulli trials or any random experiment which yields exactly two possible outcomes. The two possible results are usually called a "success", which is represented by symbol 'p' and a "failure", which is represented by symbol 'q'.

An example of Bernoulli trial is a coin flip or coin toss. Heads or tails can be defined as either a success or failure depending on the outcome you want to keep track of. During a coin flip, heads can be considered as "failure" and tails as "success". The probability of success would be 0.5 and the probability of failure would be 1-p or 1-0.5, which is also 0.5. However, it is not necessary that each Bernoulli trial's probability of success or failure have to be 50%. Plotting in a Bernoulli distribution, the probability of success is labeled on the x-axis as n=1, and failure labeled as n=O. Because of its characteristics, Bernoulli distribution is known as the simplest probability distribution that exists.