Simulations
Here are links to some cool (and instructive!) java simulations. They
are hosted at the
Dartmouth Chance
Project, an amazing resource, which is
well worth checking out in its own right (in particular, the
Chance News
section).

Central limit theorem demonstration.
This is a java applet to demonstrate, in a quite dramatic fashion, the
emergence of the normal distribution in sums of independent random
variables. The applet allows you to specify the initial distribution
by assigning probabilities for (up to) 10 values
P(0), P(1), P(2), ..., P(9). The program then computes and plots, for
given n, the distribution of a sum of n independent r.v.'s having this
distribution. It is remarkable how quickly the distribution approaches
the normal shape as one increases the value of n from n=1 (the
original distribution) to 2, 3, etc. This occurs, sooner or later,
no matter what the shape of the original distribution. For nice
symmetric distributions (e.g., uniform) the convergence to the normal
distribution is very fast; for other distributions it may take a bit
longer to see the normal distribution emerge.
 Normal
approximation to binomial distribution. A java applet that, for given values of n and p
and a given range for k, plots the binomial distribution along with
the approximating normal curve. The match is remarkably good, even if n is
relatively small.

Plot of the Binomial Distribution.
This java applet plots the binomial distribution for a given
value of p and three values of n.

Coin tossing simulation. This applet simulates a sequence of coin
tosses and plots the accumulated "scores" (1 for a head, 1 for a tail).
Back to
the Math 408 Course Webpage
Last modified Mon 14 Apr 2008 08:11:21 AM CDT