QUESTION : With an infinite number of stores, half charging $1 and half charging $2. You decide to check three stores randomly and buy from a store which has the minimum of the three prices checked. What is the expected value of the price you will pay?
Expected Value could be considered a weighted average, but it's usually not the mean of a set of numbers. It is calculated as the sum of over all possible values of n. In the case of your problem, there is a 1/8 probability you will have all $2 stores and have to pay $2, and a 7/8 probability that at least one of the three stores will be a $1 store and you have to pay $1. No other values besides $1 and $2 are possible, so the Expected Value is (1/8)*2 + (7/8)*1. In this problem, it makes sense to give this number a dollar sign.