Geometric distribution

Probability distribution

In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution of the number X {\displaystyle X} of Bernoulli trials needed to get one success, supported on N = { 1 , 2 , 3 , … } {\displaystyle \mathbb {N} =\{1,2,3,\ldots \}} ; The probability distribution of the number Y = X − 1 {\displaystyle Y=X-1} of failures before the first success, supported on N 0 = { 0 , 1 , 2 , … } {\displaystyle \mathbb {N} _{0}=\{0,1,2,\ldots \}} . These two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of X {\displaystyle X}); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.

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