An event is a subset of the sample space .

**Distribution Function**
We defined the distribution function
for a finite sample space
to be a positive
real valued function *m* that
is defined on
and
such that:

When the sample space is either finite or countably infinite we say the distribution is discrete.

To an experiment we associate a number, we either number the outcomes, or we assign winnings to them. This number is called a random variable in fact it is a function from the outcomes into the reals.

**Random Variable**:
We call the numerical outcome of a chance experiment a
random variable, and we denote it by *X*.

Example 1:

When rolling a dice the sample space is

Suppose we define the following 3 events: , , We want to define the probability of these events. If we didn't know any rules but wanted to use the computer to simulate throwing a die and counting how frequent each event was.

Here is the matlab simulation we did in class:

- Matlab Dice Example from lecture 09/24/98
- Definition of Probability 9/25
- Discrete Uniform Random Distribution
- Computer Simulation
- Problem Session,09/25/98: De Méré's Problem
- Another Matlab Example for dice game