Probability mass function: Difference between revisions

Revision as of 17:54, 23 November 2005

Revision as of 02:51, 6 February 2006

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A simple example of a probability mass function is the following. Suppose that ''X'' is the outcome of a single coin toss, assigning 0 to tails and 1 to heads. The probability that ''X'' = ''x'' is just 0.5 on the state space {0, 1} (this is a [[Bernoulli distribution|Bernoulli random variable]]), and hence the probability mass function is

:<math>f_X(x) = \begin{cases}0.5\frac{1}{2}, &x \in \{0, 1\},\\0, &x \in \mathbb{R}\backslash\{0, 1\}.\end{cases}</math>

Probability mass functions may also be defined for any discrete random variable, including [[constant random variable|constant]], [[Binomial distribution|binomial]] (including [[Bernoulli distribution|Bernoulli]]), [[negative binomial distribution|negative binomial]], [[Poisson distribution|Poisson]], [[geometric distribution|geometric]] and [[hypergeometric distribution|hypergeometric]] random variables.