Bernoulli Trials

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 Coin Sample Experiment----The experiment consists of tossing n coins, each with probability of heads p. The results are recorded on each update. You can select the number of coins  n and probability p.
See also The Dice Sample Experiment, Die Coin Experiment  and Coin Die Experiment

The Binomial Coin Experiment----The experiment consists of tossing n coins, each with probability of heads p. The number of heads X and the proportion of heads M are recorded on each update.  The density and mean of the  variable are shown in blue
in the distribution graph blue and are recorded in the distribution table. The parameters n and p can be varied with scroll bars.
Either X or M can be selected with the list box.
See also The Dice Experiment, The Binomial Timeline Experiment and The Galton Board Experiment

The Negative Binomial Experiment----The experiment consists of performing Bernoulli trials, with probability of success p,
until the k'th success occurs.  The density and moments of Y(the number of trials)  are shown in blue in the distribution graph
and are recorded in the distribution table. On each update, the empirical density and moments of Y are shown in red in the distribution graph and are recorded in the distribution table.

The Problem of Points Experiment----The experiment consists of tossing coins, each with probability of heads p, until either n heads occur or m tails occur. The event that n heads occur before m tails is indicated by the random variable I. The density of
I is shown in blue in the second graph and is recorded in the second table. On each update, the empirical density of I is shown in red in the second graph and is recorded in the second table. The parameters n, m, and p can be varied with scroll bars.
See also The Coupon Collector Experiment