Probability Distributions
In this experiment, we can simulate the occurrence of random events which
can have one of several distributions:
 An arbitrary distribution, whose values and probabilities are user
specified.
 A Gaussian (or Normal) distribution with a specified mean and standard
deviation.
 A uniform (or flat) distribution, with events equally likely to occur
anywhere within the interval from 0 to 1.
Any of these distributions can be assigned to the random variables
x, y, or z.
After the random variables x,y,z are defined, a new random variable
w(x,y,z) can be formulated.
Rules for forming expressions for w:

Operators are: +, , *, /

No more than a single operator may appear within a pair of parentheses

Constants may appear within the expression

Every time a random variable appears in an expression, a new realization
of that variable is obtained. So, if w = x+x,
then w is the sum of two realizations of a random variable whose
characteristics are defined as x.

Several functions are available

pow(x,n)a single realization of x multiplied by itself
n times

sum(x,n)n realizations of x added together

exp(x)the exponential function, e to the xth power

sin(a)where a is an expression in degrees which may involve random variables

cos(a)where a is an expression in degrees which may involve random variables

tan(a)where a is an expression in degrees which may involve random variables
This allows the user to express the following sort of problem:
If the sides of a box are measured as 20, 30, and 40
centimeters, respectively, where each measurement could have a Gaussiandistributed
error of mean 0.0 and
standard deviation of 1.0, what would be the distribution of calculated
volumes?
In this problem x would be assigned a Gaussian distribution with
mean 0.0 and standard deviation 1.0. Then,
the volume w would be expressed as w = ((20+x)*(30+x))*(40+x).
Then one can display the distribution of w over, say, 10000 realizations.
Another example:
What is the distribution of values for the sum
of three thrown dice?
Define x as an arbitrary distribution with
Pr(x) = 1,1,1,1,1,1 (i.e., each face
equally likely), and with the values of x = 1,2,3,4,5,6
(the values of the six sides). Then the sum of three thrown dice
can be expressed as w = (x+x)+x, or
w = sum(x,3)
Generate some
probability distributions.
