StudentTDistribution[ 10 ] - Wolfram|Alpha

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Input

Student's t distribution | degrees of freedom | ν = 10

Statistical properties

mean | 0
mode | 0
standard deviation | sqrt(5)/2≈1.11803
variance | 5/4 = 1.25
skewness | 0

Probability density function (PDF)

984375/8 (1/(x^2 + 10))^(11/2)

Plot of PDF

Plot of PDF

Cumulative distribution function (CDF)

P (X<=x) = (x ((8 x^8)/625 + (72 x^6)/125 + (252 x^4)/25 + 84 x^2 + 315))/(256 sqrt(10) (-x^2/10 - 1)^4 sqrt(x^2/10 + 1)) + 1/2

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