Let y denote the number of people known personally who were victims of homicide within the past 12 months. According to results from recent General Social Surveys, for a randomly chosen person in the United States the probability distribution of y is approximately P(0) = 0.91,P(1) = 0.06,P(2) = 0.02, and P(3) = 0.01.

(a) Explain why it is not valid to find the mean of this probability distribution as (0 + 1 + 2 + 3)/4 = 1.5.

(b) Find the correct mean of the probability distribution.