# SOCR Courses 2011 2012 Stat13 1 Lab2

## Contents

## Stats 13.1 - Laboratory Activity 2: Coin Die Experiment

Go to SOCR Experiments and use the scroll bar to find the Coin Die Experiment. Once you find it, click on the **About** button and read about the experiment. Answer the following questions with references to graphs where appropriate.

### Problem 1

There are two random variables (X=coin,Y=die), one parameter (p) for the coin, and the probability distribution that governs each die (green or red) involved in this experiment. Describe what each random variable represents.

- Choose a fair coin (p = 0.5), and fair dice (green and red).
- Perform 10 runs and take a snapshot
- Perform 100 runs and take a snapshot

### Problem 2

Construct the probability distribution of Y

### Problem 3

Comment on the empirical and theoretical distributions how the sample size affects them.

### Problem 4

- Reset
- Choose p = 0.8, 1 and 6 flat for the green die (0.25 0.125 0.125 0.125 0.125 0.25), and 3 and 4 flat for the red die (0.125 0.125 0.25 0.25 0.125 0.125)
- Perform 100 runs and take a snapshot

Construct the probability distribution of Y.

### Problem 5

Compute the theoretical mean of Y

### Problem 6

Find the theoretical standard deviation of Y

### Problem 7

Verify that the mean agrees with the one in the distribution column of the applet.

### Problem 8

- Reset
- Choose p = 0.2, green fair die, 2-5 flat for red die
- Perform 100 runs and take a snapshot

Construct the probability distribution of Y

### Problem 9

Comment on the empirical and theoretical distributions. Also, comment on how the coin's parameter (p) affects the theoretical distributions.

### Monte Hall Activity (Let's Make a Deal)

The Monte Hall Activity can be found here: SOCR EduMaterials Activities MontyHall and the applet is here.

Click on the **About** button and read about the experiment.

- Perform 100 runs when p = 0 and p = 1. Take a snapshot of both results.

If you are playing this game only one time, should you switch doors? Why?

- SOCR Home page: http://www.socr.ucla.edu

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