The idea in Problem 5 generalizes to give a new formula for the expected value of any nonnegative integer-valued random variable. Show that if the random variable X takes only nonnegative integers as its values then...

Asales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. the representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. she uses the given expression to model the number of club members, in hundreds, after advertising for t months.