Understanding Randomness

1. Understanding Randomness Ch. 11

2. Randomness • Can not guess outcome ahead of time • “Fair” selection between outcomes • A pain in the butt in Unit I and II • A necessary and useful tool in Unit III (and all of statistics)

3. Using Randomness We will imitate real processes to manipulate, control, and understand them using simulation

4. Simulation • The sequence of events we want to investigate is called a trial. • The basic building block of a simulation is called a component. • Trials usually involve several components. • After the trial, we record what happened—our response variable.

5. Think, Show, Tell • Thinkfirst. Know where you are headed and why. • Show your work. The mechanics of the calculation are important but can not exist on there own. • Tellyour conclusion in the context of the problem

6. Simulation Steps • Identify the component to be repeated. • Explain how you will model the component’s outcome. • Explain how you will combine the components to model a trial. • State clearly what the response variable is. • Run several trials. • Collect and summarize the results of all the trials. • State your conclusion in the context of the problem.

7. What Can Go Wrong? • Don’t overstate your case. • Beware of confusing what really happens with what a simulation suggests might happen. • Model outcome chances accurately. • A common mistake in constructing a simulation is to adopt a strategy that may appear to produce the right kind of results. • Run enough trials. • Simulation is cheap and fairly easy to do.