BUILT-IN MATHEMATICA SYMBOL

# StudentTDistribution

represents a Student distribution with degrees of freedom.

represents a Student distribution with location parameter , scale parameter , and degrees of freedom.

## DetailsDetails

• The probability density for value in a Student distribution with degrees of freedom is proportional to . »
• With location parameter and scale , follows a standard Student distribution with degrees of freedom.
• For integer , the Student distribution gives the distribution of the deviation from the true mean of the observed mean for a sample of values from a normal distribution, normalized by standard deviation of the sample.
• StudentTDistribution allows to be any real number and and to be any positive real numbers.
• StudentTDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

## ExamplesExamplesopen allclose all

### Basic Examples (8)Basic Examples (8)

Probability density function:

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Cumulative distribution function:

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Mean and variance:

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Median:

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Probability density function of a generalized Student distribution:

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Cumulative distribution function of a generalized Student distribution:

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Mean and variance of a generalized Student distribution:

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Median of a generalized Student distribution:

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