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

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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.)

posted Jun 9

## 1 Solution

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.

solution Jun 19

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