Mean and Variance of the F Distribution

The F distribution with df1 = \(n_1\) and df2 = \(n_2\) degrees of freedom has mean and variance: \(\mu = \frac{n_2}{n_2 - 2} \quad (n_2 > 2)\) \(\mathrm{Var}(X) = \frac{2 n_2^2 (n_1 + n_2 - 2)}{n_1 (n_2 - 2)^2 (n_2 - 4)} \quad (n_2 > 4)\)

mf(df1, df2)

Arguments

df1

Numerator degrees of freedom

df2

Denominator degrees of freedom

Value

List with mean and variance

References

Hogg, R.V., McKean, J., and Craig, A.T. (2018). Introduction to Mathematical Statistics. Pearson.

See also

df

Examples

mf(df1 = 5, df2 = 10)
#> $mean
#> [1] 1.25
#> 
#> $variance
#> [1] 1.35
#>