Built-in Mathematica Symbol

NormalDistribution

NormalDistribution[

,

]
represents a normal (Gaussian) distribution with mean

and standard deviation

.

NormalDistribution[]
represents a normal distribution with zero mean and unit standard deviation.

MORE INFORMATION

The probability density for value in a normal distribution is proportional to . »

NormalDistribution allows to be any real number and to be any positive real number.

NormalDistribution can be used with such functions as Mean, CDF and RandomReal. »

EXAMPLES

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Basic Examples (2)

The mean and variance of a normal distribution:

Probability density function:

The mean and variance of a normal distribution:

Probability density function:

Scope (3)

Generate a set of pseudorandom numbers that are normally distributed:

Properties based on higher-order moments:

The

quantile of a normal distribution:

Applications (5)

Compute

-values for a

-test with alternative hypothesis

:

Alternative hypothesis

:

Alternative hypothesis

:

Plot the cumulative distribution function of the random variable:

A contour plot as both

and

are varied:

Normally distributed points in the plane:

Normally distributed points in 3D:

Properties & Relations (4)

Its probability density function integrates to unity:

StudentTDistribution goes to a normal distribution as

goes to

:

LogNormalDistribution is logarithmically related to NormalDistribution:

HalfNormalDistribution density is proportional to NormalDistribution for positive values:

Possible Issues (2)

NormalDistribution is not defined when

is not a real number:

NormalDistribution is not defined when

is not a positive real number:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: