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1. The expected value is 2.3 if the payout probability distribution is payout  0 2 4 8 10  probability 0.45 0.3 0.1 0.1 0.05.

   According to the given question.

   We have the payout probability distribution.

   payout(s): 0  2  4  8  10

   Probability: 0.45  0.3  0.1  0.1  0.05

   Multiply payout to probability such that:

   0×0.45 = 0

   2 × 0.3 = 0.6

   4 × 0.1 = 0.4

   8 × 0.1 = 0.8

   10 × 0.05 = 0.5

   Therefore, the expected value of the winnings from a game with the given payout probability distribution is

   = 0 + 0.6 + 0.4 + 0.8 + 0.5

   =2.3

   Thus, the expected value is 2.3 if the payout probability distribution is payout  0 2 4 8 10  probability 0.45 0.3 0.1 0.1 0.05.

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