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[solution] » Joe Smith plays a betting game with his friends. He puts in one

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Joe Smith plays a betting game with his friends. He puts in one

Joe Smith plays a betting game with his friends. He puts in one dollar to join the game. If he wins the game, he gets $2. So his gain is $1. If he loses, he gets nothing, so his gain is ?$1. Let V be the random variable that denotes the gain (amount of money in dollars) made by Joe Smith. (Remember that a loss is counted as negative gain). The pmf of V is given below. (****I have attached the pmf table!)

Joe Smith is planning to play the game 100 times. The 100 outcomes will be independent of each other.

a) What is his expected total gain if he plays 100 times?

b) What is the variance of his total gain?

c) Use the Central Limit Theorem to compute the probability that his total gain will be positive.


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