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6.2 Exercise 14

Avg difficulty 2.5

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 = 3 I A + 4 I B + 6 I C - 6 , with P ( A ) = 0 . 5 , P ( B ) = 0 . 4 , P ( C ) = 0 . 3 X = 3 I_{A} + 4 I_{B} + 6 I_{C} - 6 , \text{with} P \left(A\right) = 0 . 5 , P \left(B\right) = 0 . 4 , P \left(C\right) = 0 . 3

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

Pfeiffer, Applied Probability, 6.2 Problems on Random Variables and Probabilities, exercise 14

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.