1. Probability Experiment:

1. Construct a probability distribution for the sums shown on the top faces when two dice are rolled. (Hint: X can be 2,3,4,...,12.) You might want to look at Example 4-1 on page 187 and then Figure 4-1 on page 187 to help you find the theoretical probabilities of X. Usingthe probability distribution you constructed, find the mean number of spots.
2. Roll two dice 50 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for your 50 sums. Using theprobability distribution you constructed, find the mean number of spots. (If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Place the pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers.)
3. Isthe mean in (b) close to the mean in (a)? Explain why there is a difference in the two means or why they are the same.