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Two balls are chosen randomly from a basket containing 8 white, 4 black and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings.

(a) What are the possible values of X ?
(b) What are the probabilities associated with each value?
(c) Do you expect to win? By how much?
(d) Obtain the moment generating function for the obtained probability function.
(e) Verify your answer in (c) using your result in (d).

 

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