Normal Distribution graph Chi-Square Distribution graph


The experiment simulates a random sample \(\boldsymbol{X} = (X_1, X_2, X_3) \) from the normal distribution with mean 0 and variance \( a^2 \). Random variable \( Z \) is the magnitude of the random vector \(\boldsymbol{X}\):

\[ Y = \sqrt{X_1^2 + X_2^2 + X_3^2} \]

which has the Maxwell-Boltzmann distribution with scale parameter \( a \). On each run, the applet shows the normal sample in the graph on the left. The Maxwell-Boltzman 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 parameter \(a\) can be varied with the input control.