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Statistics[Distributions][Bernoulli] - Bernoulli distribution

Calling Sequence

Bernoulli(p)

BernoulliDistribution(p)

Parameters

p

-

probability of success

Description

• 

The Bernoulli distribution is a discrete probability distribution with probability function given by:

ft=piecewiset=0,1p,t=1,p,0

  

subject to the following conditions:

0p,p1

• 

The Bernoulli distribution comes about as a consequence of a single Bernoulli trial .  Success of the Bernoulli trial is indicated with x=1 and failure is indicated with x=0, where a success occurs with probability p.  The parameter p is also referred to as the Bernoulli probability parameter.

• 

Note that the Bernoulli command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics:

X:=RandomVariableBernoullip:

ProbabilityFunctionX,0

1p

(1)

ProbabilityFunctionX,1

p

(2)

MeanX

p

(3)

VarianceX

p1p

(4)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

References

  

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

  

Johnson, Norman L.; and Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.


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