Geometric Distribution
The distribution on models the number of Bernoulli trials needed to get the first success:
For example, it models tosses of a biased coin with heads probability up to the first heads; the probabilities sum to as a geometric series.
Definition 2.23 (Geometric Distribution)
A geometric distribution models the number of Bernoulli trials needed to get the first success, where each trial has success probability .
The geometric distribution with parameter is defined by
Note that,
This models, for example, the number of times we need to toss a biased coin with heads probability until we get the first heads.
Related
Stated in
- Definition 2.23 (Geometric Distribution)§2.5 Discrete Probability Distributions