The “last name” effect in purchasing. The Journal of Consumer Research (Aug. 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. Do you believe the probability distribution in part a is realistic? Explain. How might you go about estimating the true probability distribution for x?