3. There are five closed boxes on a table. Three of the boxes have nice prizes inside. The other two do not. You open boxes one at a time until you find a prize (and then you stop). Let X be the number of boxes you open, including the last one that contains a prize.(i) Find the probability mass function of x.(ii) Find E[X].(iii) Find Var(X).(iv) Suppose the prize inside each of the three good boxes is 100, but each empty box you open costs you100. What is your expected gain or loss in this game?
3. There are five closed boxes on a table. Three of the boxes have nic…
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