SOCR EduMaterials Activities DiceExperiment

This is an activity to explore the distribution of various discrete random variable when \( n \) dice are rolled.

Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Dice Experiment. Once you find it, click on the About button and read about the experiment. Below you can see the distribution of the sum (\( Y \)) of the two numbers shown when 2 dice are rolled.

Answer the following questions:

a. There are five random variables (\( Y, M, U, V, Z \)) and two parameters \( n, p \)) involved in this experiment. Describe what each one represents.

b. Choose \( n=3 \). Find the probability distribution for each one of the random variables \( Y, M, U, V, Z \), compute the mean and standard deviation for each one of them, and verify that they agree with the ones in the applet.

c. Choose \( Y, \ n=3 \), fair dice, perform 100 runs, take a snapshot and comment.

d. Reset. Choose \( M, \ n=3 \), fair dice, perform 100 runs, take a snapshot and comment.

d. Reset. Choose \( U, \ n=3 \), fair dice, perform 100 runs, take a snapshot and comment.

e. Reset. Choose \( V, \ n=3 \), fair dice, perform 100 runs, take a snapshot and comment.

g. Reset. Choose \( Z, \ n=3 \), fair dice, perform 100 runs, take a snapshot and comment.

h.Reset. Change \( p \) to 1-6 Flat (1,6 each has probability 0.25, and 2,3,4,5, each has probability 0.125). Find the probability distribution of \( Y \) when \( n=3 \) dice are rolled and verify that it agrees with the one in the applet. Run the experiment 100 times, take a snapshot and comment.