Bernoulli Distribution

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Bernoulli Distribution

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The Bernoulli distribution is the simplest
discrete probability distribution
It models a single trial that results in two possible
outcomes:
• Success (1) with probability p
• Failure (0) with probability 1−p

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Definition and Parameters
A Bernoulli random variable X is defined as:

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Probability Mass Function (PMF)
The probability function (PMF) of X
is:

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Cumulative Distribution
Function (CDF)
The CDF shows the probability that X is less than or equal to a value x:

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MEAN AND VARIANCE

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Other Statistical Measures

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Related Distributions

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Graph of the Probability Function

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Application
s outcomes:
Modeling binary
Product test
(Defective/Non
-defective)
Exam result
(Pass/Fail)
Coin toss

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Summary

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