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Bernoulli Distribution

Bernoulli Distribution#

TODO

Bernoulli Random Variable#

A Bernoulli random variable Y is defined for experiments where the only outcomes are “success” and “failure”, which we denote s and f, respectively. The sample_space for a Bernoulli random variable is given by,

S = \{ s, f \}

A Bernoulli random variable Y takes on the value of 1 when a success occurs and it takes on the value of 0 when a failure occurs. In other words,

Y \in \{ 0, 1 \}

Probability Density#

TODO

P(Y = 1) = p

By the Law of Complements, the probability of a 0 is,

P(Y = 0) = 1 - p

We can summarize these results as follows,

P(Y = y) = \begin{array}{ c l } p & \quad \textrm{if } y = 1 \\ 1 - p & \quad \textrm{if } y = 0 \end{array}

Distribution#

TODO

Remarks#

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