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## Sample Space 09/24

The set of all possible outcomes is called the sample space and noted .

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:

Next: Matlab Dice Example from Up: Basic Concepts Previous: Probability
Susan Holmes
1998-12-07