Student[Statistics]
NormalRandomVariable
normal (Gaussian) random variable
Calling Sequence
Parameters
Description
Examples
References
Compatibility
NormalRandomVariable(mu, sigma)
mu
-
distribution mean
sigma
scale parameter
The normal random variable is a continuous probability random variable with probability density function given by:
ft=2ⅇ−t−μ22σ22πσ
subject to the following conditions:
μ::real,0<σ
The normal variate Normal(mu,sigma) is related to the standardized variate Normal(0,1) by Normal(0,1) ~ (Normal(mu,sigma)-mu)/sigma.
withStudentStatistics:
X≔NormalRandomVariableμ,σ:
PDFX,u
2ⅇ−u−μ22σ22πσ
PDFX,0.5
0.3989422802ⅇ−0.50000000000.5−1.μ2σ2σ
MeanX
μ
VarianceX
σ2
Y≔NormalRandomVariable3,5:
PDFY,x,output=plot
CDFY,x
12+erfx−32102
CDFY,3,output=plot
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.
The Student[Statistics][NormalRandomVariable] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
Statistics[Distributions][Normal]
Statistics[RandomVariable]
Student
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