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.

Random Walk----The experiment consists of tossing n fair coins. The position of the random walk after j tosses is the number of heads minus the number of tails. Three random variables( the final position,the maximum position and the time of the last zero) are recorded and their densities and means are shown.
See also The Ballot Experiment

Poisson Experiment ----The experiment is to run a Poisson process until time t. The arrivals are shown, and the number of
arrivals N is recorded and its density and mean  is shown.
See also The Exponential Experiment and The Gamma Experiment

The Two-Type Poisson Experiment----The experiment is to run a Poisson process until time t. Each arrival is type 1 with probability p or type 0 with probability 1 - p.The number of type 1 arrivals M and the number of type 0 arrivals W are recorded and their densities and means are shown.

The Two-Dimensional Poisson Experiment----The experiment is to run a Poisson process in the plane, and record the number of points N in the square [0, w]2.  The number of points N is recorded and the density and moments of N is shown.

Red and Black Game( Gambler Ruin Problem)----A player starts with an initial fortune x and bets (at even stakes) on independent trials for which the probability of winning is p. The player must continue until she is either ruined or reaches
a fixed target fortune a.
See also Red and Black Experiment