X Distribution graph Y Distribution graph F Distribution graph

#### Description

The experiment simulates a random sample $$\boldsymbol{X} = (X_1, X_2, \ldots, X_m)$$ of size $$m$$ from the normal distribution with mean $$\mu$$ and variance $$\sigma^2$$, and a random sample $$\boldsymbol{Y} = (Y_1, Y_2, \ldots, Y_n)$$ of size $$n$$ from the normal distribution with mean $$\nu$$ and standard deviation $$\tau$$. The samples are independent. Random variable $$V$$ is

$V = \frac{S_X^2 / \sigma^2}{S_Y^2 / \tau^2}$

where $$S_X^2$$ and $$S_Y^2$$ are the sample variances of $$\boldsymbol{X}$$ and $$\boldsymbol{Y}$$, repsectively. Random variable $$V$$ has the $$F$$ distribution with $$m$$ degrees of freedom in the numerator and $$n$$ degrees of freedom in the denominator. On each run, the applet shows the normal samples in the first two graphs. The $$F$$ distribution is shown in the last graph and in the second table. As the experiment runs, the empricial density and moments are shown in this graph and recorded in this table. The parameters $$\mu$$, $$\sigma$$, $$\nu$$, $$\tau$$, $$m$$ and $$n$$ can be varied with the input controls.