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Write What is a simulation ? Why would we use one? What are the pieces of a simulation? Give two examples of a situation where you might use a simulation in order to answer a question. What are the possible outcomes in each simulation’s simulated condition?

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Write

What is a simulation? Why would we use one? What are the pieces of a simulation?

Give two examples of a situation where you might use a simulation in order to answer a question. What are the possible outcomes in each simulation’s simulated condition?

So how do we design and perform a simulation?
• In order to see how this is done, we’re going to use the situation described yesterday:

“A cereal manufacturer is putting photos of famous athletes in its boxes at random. 20 % of boxes contain a picture of Tiger Woods, 30 % a picture of Lance Armstrong, and the rest a picture of Serena Williams.

How many boxes will you have to buy in order to get every picture?”

Let’s identify what’s going on here.
• Simulated component: buying a box of cereal
• Outcomes:
• Tiger – 20 % of the time
• Serena – 50 % of the time
• Lance – 30 % of the time
• Trial: the sequence of boxes bought before all 3 pictures show up
Random Data from the TI-84
• MATH 
• PRB 
• 5: randInt
• (low, high, how many?)
• If you leave how many blank, just 1 is produced.
• For more than one simulated component, just press ENTER repeatedly
So what were our steps here?
• Identify the component to be repeated.
• Decide how we will model the outcome using random data.
• Decide how we will simulate the trial.
• State clearly what the response variable is – that is, the ‘thing’ we’re actually interested in.
• Run several trials – the more the better.
• Analyze the response variable.
• State our conclusion – in the context of the problem.
Identify the component to be repeated.

Decide how we will model the outcome using random data.

Decide how we will simulate the trial.

State clearly what the response variable is – that is, the ‘thing’ we’re actually interested in.

Run several trials – the more the better.

Analyze the response variable.

State our conclusion – in the context of the problem.

Opening boxes of cereal will be repeated.

0,1 = Tiger 2,3,4 = Lance 5+ = Serena

Pretend to open boxes until we get all 3 pictures

How many boxes it takes before we have gotten at least one of each of the pictures.

We all did this using data generated by the TI-84.

We took the mean of our trials.

We were restrained in our statement of our conclusion.

So what were our steps here?
What’s next?
• Well, on Monday, we’ll design and perform simulations in our groups.
• On Tuesday, we’ll finish these simulations up, and we’ll present our results.
• After that, we’ll start talking about samples and bias – two very important topics that can get in the way of the randomness and fairness that we’ve been talking about.

### Have a nice weekend!

No homework!

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