Uniform Distribution graph Irwin-Hall Distribution graph


The experiment simulates a random sample \( (X_1, X_2, \ldots, X_n) \) of size \( n \) from the uniform distribution on the interval \( [0, 1] \). Random variable \( Y = X_1 + X_2 + \cdots + X_n \) has the Irwin-Hall distribution with parameter \( n \). On each run, the applet shows the uniform sample in the graph on the left. The Irwin-Hall 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 \(n\) can be varied with the input control.