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There are six closed boxes on the table. Three of the boxes have prizes inside while the other three are empty. You open the boxes one at a time randomly until you find a price. Let X be the number of boxes you open.
1. Find the probability mass function of X.
2. Find Var(X) = E[X2] - E[X]2.
3. Suppose the prize inside each of the three boxes is $100, but each empty box you open costs you $100. What is your expected gain or loss in this game?
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