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Student[Statistics]

  

Probability

  

compute the probability of an event

 

Calling Sequence

Parameters

Description

Computation

Examples

References

Compatibility

Calling Sequence

Probability(X, numeric_option, inert_option)

Parameters

X

-

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

numeric_option

-

(optional) equation of the form numeric=value where value is true or false

inert_option

-

(optional) equation of the form inert=value where value is true or false

Description

• 

The Probability function 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.

• 

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

Computation

• 

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

• 

If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

• 

By default, the probability of an event is computed according to the rules mentioned above. To always compute the probability numerically, specify the numeric or numeric = true option.

Examples

withStudentStatistics:

Compute the probability of the normal random variable with parameters a and b.

NNormalRandomVariablea,b:

Probabilityx<N

12erfxa22b2

(1)

Use numeric parameters.

ProbabilityNormalRandomVariable2&comma;3<x

12+erfx2262

(2)

ProbabilityNormalRandomVariable2&comma;3<1

12erf262

(3)

ProbabilityNormalRandomVariable2&comma;3<1&comma;&apos;numeric&apos;

0.369441340181764

(4)

Compute the probability that a exponential random variable lies in the range of (4,7). Instead of calling the function as Probability(4 < E < 7), the right way of using the function is Probability({4<E,E<7}).

EExponentialRandomVariable5&colon;

Probability4<E&comma;E<7

&ExponentialE;75+&ExponentialE;45

(5)

Consider a random variable that is made up by two other random variables.

X2BernoulliRandomVariable12&plus;ExponentialRandomVariable3&colon;

ProbabilityX<5.0

0.7216224780

(6)

Use the inert option.

ProbabilityX<5&comma;inert

limu5_k=010_k<001<_k12otherwiseu2_k0_t<0&ExponentialE;_t33otherwise&DifferentialD;_t

(7)

References

  

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][Probability] command was introduced in Maple 18.

• 

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

See Also

Statistics[Probability]

Student

Student[Statistics]

Student[Statistics][CumulativeDistributionFunction]

Student[Statistics][ProbabilityDensityFunction]

Student[Statistics][RandomVariable]