Direction:  For each following applet, the density and moments of  the random variable are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density and moments are shown in red in the distribution graph and are recorded in the distribution table. The parameter can be varied with a scroll bar.Press "Step" button
to show each simulation.You may see a serial of simulation by choosing the number of simulation from the "stop freq" list box(the default number is 10) and pressing "run" button.Renew or stop the process by choosing "reset" button or "stop" button,respectively.

The Finite Order Statistic Experiment----The experiment consists of selecting n balls at random (without replacement) from a population of N balls, numbered from 1 to N. For i = 1, 2, ..., n, the i'th smallest number in the sample, X(i) (the i'th order statistic), is recorded on each update.  The distribution and moments of X(k) are shown in the blue in the distribution graph . When the simulation runs, the empirical distribution and moments of X(k) are shown in red in the distribution graph.
See also Order Statistic Experiment

The Matching Experiment----The matching experiment is to randomly permute n balls, numbered 1 to n. A match occurs whenever the ball number and the position number agree. The matches are shown in red. The number of matches N is recorded on each update.

The Birthday Experiment----The birthday experiment is to draw a random sample of size n with replacement from a population of size N.  the indicator variable of  the event that there is at least one duplication in the sample t is denoted I.
See also The General Birthday Experiment