A simple example of the difference between ideal and non- ideal conditions is the rolling of a die.
a. Calculate the expected value of a single roll of a fair die.
b. Now suppose that you are unsure whether the die is fair. How would you then calculate the expected value of a single roll?
c. Continuing part b, now roll the die four times. You obtain 6, 4, 1, 3. Does this information affect your belief that the die is fair? Explain.