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Student[Statistics]

  

BernoulliRandomVariable

  

Bernoulli random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

BernoulliRandomVariable(p)

Parameters

p

-

probability of success

Description

• 

The Bernoulli random variable is a discrete probability random variable with probability function given by:

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

  

subject to the following conditions:

0p,p1

• 

The Bernoulli random variable 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.

Examples

withStudent[Statistics]:

XBernoulliRandomVariablep:

ProbabilityFunctionX,0

1p

(1)

ProbabilityFunctionX,1

p

(2)

MeanX

p

(3)

VarianceX

p1p

(4)

YBernoulliRandomVariable13:

ProbabilityFunctionY,x,output=plot

CDFY,x

&lcub;0x<023x<11otherwise

(5)

CDFY&comma;1&comma;output&equals;plot

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.

Compatibility

• 

The Student[Statistics][BernoulliRandomVariable] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

Statistics[Distributions][Bernoulli]

Student

Student[Statistics]

Student[Statistics][RandomVariable]

 


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