F Distribution and Moment Boundaries

The F-distribution arises as the ratio of two independent chi-square random variables, each divided by its respective degrees of freedom. It plays a fundamental role in analysis of variance (ANOVA) and testing hypotheses about variances.

Experiment

Observe how the shape and properties of the F-distribution change as you adjust the degrees of freedom.

1. Open the F Distribution and Moment Boundaries module.
2. Select Numerator df to 4 and Denominator df to 2. Notice that the mean and variance become undefined because the heavy tail drops off too slowly.
3. Change the Numerator df to 1 and the Probe x to 0. Notice that the density near x=0 becomes unbounded (it shoots up to infinity).