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Statistics[Distributions]

  

DiscreteUniform

  

discrete uniform distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

DiscreteUniform(a, b)

DiscreteUniformDistribution(a, b)

Parameters

a

-

lower bound parameter

b

-

upper bound parameter

Description

• 

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

ft&equals;piecewiset<a&comma;0&comma;tb&comma;1ba&plus;1&comma;0

  

subject to the following conditions:

a<b

• 

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

Examples

withStatistics&colon;

XRandomVariableDiscreteUniforma&comma;b&colon;

ProbabilityFunctionX&comma;u

&lcub;0u<a1b&plus;a1ub0otherwise

(1)

ProbabilityFunctionX&comma;4

&lcub;04<a1b&plus;a14b0otherwise

(2)

MeanX

12a&plus;12b

(3)

VarianceX

112a2&plus;112b2&plus;16b16ab16a

(4)

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.

See Also

Statistics

Statistics[Distributions]

Statistics[Distributions][Uniform]

Statistics[RandomVariable]

 


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