Normal Distribution graph Student Distribution graph


The experiment simulates a random sample \( (X_1, X_2, \ldots, X_n) \) of size \( n \) from the normal distribution. Random variable

\[ T = \frac{M - \mu}{S / \sqrt{n}} \]

where \( M \) is the sample mean and \( S \) is the sample variance, has the student \( t \) distribution with \( n \) degrees of freedom. On each run, the applet shows the normal sample in the graph on the left. The \( t \) 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.