You are out shopping with $N, and you find an item whose price has a random value between $0 and $N.

Question

You are out shopping one day with $N, and you find an item whose price has a random value between $0 and $N. You buy as many of these items as you can with your $N. What is the expected value of the money you have left over?

(Assume that $N is large compared to a penny, so that the distribution of prices is essentially continuous.)

Answer 1

expected value of the item=average of all the random numbers between 0 and N which is N/2. Hence he can buy 2 of these items and
he will be left with nothing.