# SOCR Courses 2011 2012 Stat13 1 Lab2

(Difference between revisions)
 Revision as of 18:21, 16 November 2011 (view source)IvoDinov (Talk | contribs) (Created page with '== Stats 13.1 - Laboratory Activity 2: Coin Die Experiment== Go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] …')← Older edit Current revision as of 23:43, 24 January 2012 (view source)IvoDinov (Talk | contribs) m (→Problem 1) (20 intermediate revisions not shown) Line 4: Line 4: ===Problem 1=== ===Problem 1=== - There are two random variables (X,Y ), 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. + 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 fair coin (p = 0.5), and fair dice (green and red). + * Choose a fair coin (p = 0.5), and fair dice (green and red). * Perform 10 runs and take a snapshot * Perform 10 runs and take a snapshot * Perform 100 runs and take a snapshot * Perform 100 runs and take a snapshot Line 16: Line 16: Comment on the empirical and theoretical distributions how the sample size affects them. Comment on the empirical and theoretical distributions how the sample size affects them. + ===Problem 4=== * Reset * Reset - * Choose p = 0.8, 1-6 flat for the green die, 3-4 flat for the red die + * 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 + * Perform 100 runs and take a snapshot - + - + - ===Problem 4=== + - Construct the probability distribution of Y + + Construct the probability distribution of Y. ===Problem 5=== ===Problem 5=== - Compute the mean of Y + Compute the theoretical mean of Y ===Problem 6=== ===Problem 6=== - Compute the standard deviation of Y + Find the theoretical standard deviation of Y ===Problem 7=== ===Problem 7=== - Verify that these numbers agree with the ones in the [http://socr.ucla.edu/htmls/exp/Coin_Die_Experiment.html applet]. + Verify that the mean agrees with the one in the distribution column of the [http://socr.ucla.edu/htmls/exp/Coin_Die_Experiment.html applet]. + + ===Problem 8=== * Reset * Reset * Choose p = 0.2, green fair die, 2-5 flat for red die * Choose p = 0.2, green fair die, 2-5 flat for red die * Perform 100 runs and take a snapshot * Perform 100 runs and take a snapshot - ===Problem 8=== Construct the probability distribution of Y Construct the probability distribution of Y Line 46: Line 45: The Monte Hall Activity can be found here: [[SOCR EduMaterials Activities MontyHall]] and the [http://socr.ucla.edu/htmls/exp/Monty_Hall_Experiment.html applet is here]. The Monte Hall Activity can be found here: [[SOCR EduMaterials Activities MontyHall]] and the [http://socr.ucla.edu/htmls/exp/Monty_Hall_Experiment.html 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?

## 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.

• 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?