A radio show conducts a game according to the following rules. A number between 1 and 100 is selected at random, and the disc jockey announces what number is chosen. Call it n. The announcer then randomly selects a number between 1 and n and asks that the rst caller guess the value of the second number chosen. Assuming that the caller's guess is equally likely to be any number between 1 and n, determine the expected value of the number guessed by the caller.