Normal Distribution graph Chi-Square Distribution graph


The experiment simulates a random sample \( (X_1, X_2, \ldots, X_n) \) of size \( n \) from the normal distribution with mean \( \mu \) and variance \( \sigma^2 \). Random variable \( V \) is the sum of the squares of the standard scores:

\[ V = \sum_{i=1}^n \left(\frac{X - \mu}{\sigma}\right)^2 \]

which has the chi-square distribution with \( n \) degrees of freedom. On each run, the applet shows the normal sample in the graph on the left. The chi-square distribution is shown in the graph and table on the right. As the experiment runs, the empricial density and moments are shown in this graph and recorded in this table. The parameters \( \mu \), \( \sigma \), and \(n\) can be varied with the input controls.