P(X=x)=px(1−p)1−xfor x∈{0,1}cap P open paren cap X equals x close paren equals p to the x-th power open paren 1 minus p close paren raised to the 1 minus x power space for x is an element of the set 0 comma 1 end-set : Variance : Standard Deviation : Real-World Examples
The Bernoulli distribution is the simplest discrete probability distribution, modeling a single trial—called a —that has exactly two possible outcomes: "success" and "failure" . Core Concept and Mathematical Definition A random variable bernoulli distribution
follows a Bernoulli distribution if it can take only two values, typically denoted as (success) and (failure). The PMF is given by:
: The probability of success is denoted by , and the probability of failure by . The PMF is given by: bernoulli distribution