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Student[Statistics]

  

GeometricRandomVariable

  

geometric random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

GeometricRandomVariable(p)

Parameters

p

-

probability of success

Description

• 

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

ft=0t<0p1ptotherwise

  

subject to the following conditions:

0<p,p1

• 

The geometric random variable has the lack of memory property: the probability of an event occurring in the next time interval of an exponential random variable is independent of the amount of time that has already passed.

• 

The geometric variate is a special case of the NegativeBinomial variate with number of trials parameter x=1.

• 

The continuous analog of the geometric variate is the Exponential variate.

• 

Note that the distribution above is for the number of failures before the first success. The other common convention is for the number of trials with the last being the first success. That is, the other convention would have p1pt1 in the probability function.

Examples

withStudentStatistics&colon;

XGeometricRandomVariablep&colon;

ProbabilityFunctionX&comma;u

0u<0p1puotherwise

(1)

ProbabilityFunctionX&comma;2

p1p2

(2)

MeanX

1pp

(3)

VarianceX

1pp2

(4)

YGeometricRandomVariable14&colon;

ProbabilityFunctionY&comma;x&comma;output&equals;plot

CDFY&comma;x

0x<0134x+1otherwise

(5)

CDFY&comma;5&comma;output&equals;plot

References

  

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

  

Johnson, Norman L.; 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][GeometricRandomVariable] command was introduced in Maple 18.

• 

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

See Also

Statistics[Distributions][Geometric]

Student

Student[Statistics]

Student[Statistics][RandomVariable]