# Introduction to Probability Models

## Random Variables

A * random variable * is a numerical outcome of a random
experiment.
For example, we could consider **X** the number of spots on the
roll of a die. Or, we could roll 6 dice and let **X**
be the sum of all six values.
The * distribution * of a random variable is the collection
of possible outcomes along with their probabilities. This may be
described by a table, a formula, or a probability histogram.
If we repeat an experiment many times, we can calculate the *
sample histogram*, which is a bar chart showing the number of
times each value of **X** was observed. This should
give us an idea of the probability histogram.

In the following applet, the sample histogram for the random variable
**X**, the sum of the values showing on the dice, is
plotted.
The red plot shows the expected number of occurences of **X**,
calculated as (number of rolls) times P(**X**=x),
where P(**X**=x) is the probability
that **X** takes on the value x

### Note

To change the number of dice, check the appropriate box

### Source Code

Other applets related to probability.

Please send comments on this applet to

*cstanton@csusb.edu*