he Journal of Consumer Research (August 2011) published a study demonstrating the "last name" effect-i.e., the tendency for consumers with last names that begin with a later letter of the alphabet to purchase an item before consumers with last names that begin with earlier letters. To facilitate the analysis, the researchers assigned a number, x, to each consumer based on the first letter of the consumer's last name. For example, last names beginning with "A" were assigned x = 1; last names beginning with "B" were assigned x = 2; and last names beginning with "Z" were assigned x = 26.
a. If the first letters of consumers' last names are equally likely, find the probability distribution for x.
b. Find E(x) using the probability distribution, part a. If possible, give a practical interpretation of this value.
c. Do you believe the probability distribution, part a, is realistic? Explain. How might you go about estimating the true probability distribution for x?