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In: Statistics and Probability

In a lottery game a player chooses four digits (digits can repeat, for instance 0, 2,...

In a lottery game a player chooses four digits (digits can repeat, for instance 0, 2, 0, 2 is a valid choice) and bet $1 that all four of them will arise in the four digit number drawn from the lottery. It isn’t necessary that the order will be the same: if a player selects 2, 6, 7, 8 the selection of 8, 2, 7, 6 means he won. Player gets $200 if he wins.

1. What is the probability of winning?

2. What is the probability mass function of X, the net earnings in one game?

3. What are the mean and standard deviation of net earnings?

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