# Bernoulli distribution

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Related to Bernoulli random variable: binomial random variable, Poisson random variable

## Bernoulli distribution

[ber‚nü·lē dis·trə′byü·shən]
(statistics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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From a statistical point of view assumption 5 states the following: Each QCS conditional proportion p(X=x [where] Y=y); x=0,1; y=1,2,3 estimates true probability P(X=x [where] Y=y); x=0,1; y=1,2,3 which is the parameter of Bernoulli random variables X [where] Y=y, X=0,1; y=1,2,3.
For d = 0,1,2, 3, and i = 1, ..., m, the process {[[gamma].sup.(i).sub.d,k]}.sub.k[greater than or equal to]1] is a sequence of independent Bernoulli random variables with known probabilities [mathematical expression not reproducible].
The probability that any k of the Bernoulli random variables take on the value 1 is given in the following theorem which shows that the pmf of [S.sub.n] is essentially determined by the quantities [a.sub.k](p), k = 1, ..., n, which in turn can be specified quite generally as input to the model.

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