probability -- cumulative distribution function

Synopsis

Usage:

probability_X x
Inputs:
- X, a probability distribution,
- x, a real number,
Optional inputs:
- LowerTail => a Boolean value, default value true
Outputs:
- a real number,

Description

The cumulative distribution function of the probability distribution, i.e., the lower tail probability \(F_X(x) = P(X \leq x)\).

i1 : Z = normalDistribution()

o1 = N(0,1)

o1 : ContinuousProbabilityDistribution

i2 : probability_Z 1.96

o2 = .97500210485178

o2 : RR (of precision 53)

If the LowerTail option is false, then it instead computes the value of the survival function, i.e., the upper tail probability \(S_X(x) = P(X > x)\).

i3 : probability_Z(1.96, LowerTail => false)

o3 = .0249978951482204

o3 : RR (of precision 53)

Ways to use probability :

probability(DiscreteProbabilityDistribution,Constant)
probability(DiscreteProbabilityDistribution,Number)
probability(ProbabilityDistribution,Constant)
probability(ProbabilityDistribution,Number)

For the programmer

The object probability is a method function with options.