Refer to Example 6.2 and the outcome x of a $5 wager in craps. We found the sampling distributions of the sample mean x and the sample median M for random samples of n = 3 dice rolls from a population defined by the following probability distribution:

x -5 0 5 LO6 p1x2 19 69 29 The sampling distributions of x and M were found to be as follows:

x -5 -3.33 -1.67 0 1.67 3.33 5 p1x 2 1729 18729 114729 288729 228729 72729 8729 M -5 0 5 p1M2 25729 612729 92729

a. Show that x is an unbiased estimator of m in this situation.

b. Show that M is a biased estimator of m in this situation.