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,
\[\begin{split}P(Y = y) = \begin{array}{ c l }
p & \quad \textrm{if } y = 1 \\
1 - p & \quad \textrm{if } y = 0
\end{array}\end{split}\]
Distribution#
TODO
Remarks#
TODO