Properties of the Distribution

Calculation of Mean and Variance

To calculate the mean of the F distribution, we can integrate f *(F PDF), per the definition of mathematical expectation.

> restart;

> with(plots, display):

> f:=x->FPDF(nu[1],nu[2],x);

> EX:=int(x*f(x),x=0..infinity);

The expected value given above is only valid for , otherwise the expected value does not exist.

Calculating Var(X), the variance of the F ( ) distribution. We will employ the formula: Var(X) = E( ) -

> E_X_SQ:=int((x^2)*f(x),x=0..infinity);

> VarX:=simplify(E_X_SQ-EX^2);

The variance given above is only valid for , otherwise the variance does not exist.

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