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Statistics[Probability] - compute the probability of an event
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Calling Sequence
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Probability(X, options)
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Parameters
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X
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algebraic, relation, or set of algebraics and relations, each involving at least one random variable; an event
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options
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(optional) equation of the form numeric=value; specifies options for computing the probability density function of a random variable
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Description
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The Probability command computes the probability of the event X.
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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.
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Computation
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By default, all computations involving random variables are performed symbolically (see option numeric below).
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Options
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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.
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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.
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Examples
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Compute the probability of the normal distribution.
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Compute the probability that the product of 3 independent random variables uniformly distributed on between 0 and 1 is less than t.
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![X := [seq(RandomVariable(Uniform(0, 1)), i = 1 .. 4)]](/support/helpjp/helpview.aspx?si=4688/file02919/math127.png)
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![Y := X[1]*X[2]*X[3]](/support/helpjp/helpview.aspx?si=4688/file02919/math131.png)
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![PIECEWISE([0, t <= 0], [(1/2)*ln(t)^2*t-t*ln(t)+t, t <= 1], [1, 1 < t])](/support/helpjp/helpview.aspx?si=4688/file02919/math138.png)
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Compute the probability that the distance between two points randomly chosen from a 1x1 square is less than 1.
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![Z := ((X[1]-X[3])^2+(X[2]-X[4])^2)^(1/2)](/support/helpjp/helpview.aspx?si=4688/file02919/math144.png)
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References
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Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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Download Help Document
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