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Statistics

  

Probability

  

compute the probability of an event

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

Calling Sequence

Probability(X, options)

Parameters

X

-

algebraic, relation, or set of algebraics and relations, each involving at least one random variable; an event

options

-

(optional) equation of the form numeric=value; specifies options for computing the probability density function of a random variable

Description

• 

The Probability command computes the probability of the event X.

• 

The first parameter, X, is an event consisting of a relation or set of relations. An algebraic expression is interpreted as an equation set to zero. Each relation must involve at least one random variable. All random variables in X are considered independent. A set is interpreted as the intersection of the events of each of its members.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Options

  

The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the probability density function is computed using exact arithmetic. To compute the probability density function numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the probability of the normal distribution.

XRandomVariableNormal0,1:

ProbabilityX2<1

erf122

(1)

ProbabilityX2<1&comma;&apos;numeric&apos;

0.682689492137086

(2)

Compute the probability that the product of 3 independent random variables uniformly distributed on between 0 and 1 is less than t.

XseqRandomVariableUniform0&comma;1&comma;i&equals;1..4&colon;

YX1X2X3&colon;

ProbabilityY<t

&lcub;0t012lnt2ttlnt&plus;tt111<t

(3)

Compute the probability that the distance between two points randomly chosen from a 1x1 square is less than 1.

ZX1X32&plus;X2X4212&colon;

ProbabilityZ<12

2996&plus;14&pi;

(4)

References

  

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[Computation]

Statistics[CumulativeDistributionFunction]

Statistics[Distributions]

Statistics[ProbabilityDensityFunction]

Statistics[RandomVariables]