(Answered) Question a gambler places three bets he puts down two

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Question: A gambler places three bets. He puts down two dollars for each bet. He picks up three dollars (his original bet plus one dollar) if he wins the first bet, four dollars if he wins the second bet, and six dollars if he wins the third. His net winning can be represented by the random variable

X = 3I_A + 4I_B + 6I_C - 6, with P(A) = 0.5, P(B) = 0.4, P(C) = 0.3

Assume the results of the games are independent. Determine the distribution for X.

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