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Unformatted text preview: Homework 5 Solutions Yicheng Kang October 14, 2010 6.2 a) The probabilities for each possible outcome in the sample space are the same:1/36. There is only one instance in which the maximum is one. Thus, the probability is 1/36. There are three instances in which the maximum is two. Thus, the probability is 3/36. b)These probabilities satisfy the two conditions for a probability distribution: P ( x ) 1; and X P ( x ) = 1 . 6.4 a) P (4) = 0 . 20; P (3) = 0 . 40; P (2) = 0 . 30; P (1) = 0 . 10 . b) mean = 1 . 10 + + 4 . 20 = 2 . 70 . 6.6 a) Your 3digit number only matches one of the 1000 points, so P (500) = 1 / 1000. b) P (0) = . 999 and P (500) = . 001 c)mean= 0( . 999) + 500( . 001) = . 50. You expected return ono a one dollar bet is 0.5 dollar. 1 6.10 a) b) P ( x 50 , 000) = P (50 , 000) + P (20 , 000) = 0 . 20 + 0 . 10 = 0 . 30. x P(x) $ 80,000 0.70 $50,000 0.20 $20,000 0.10 b) = 80 , 000(0 . 70)+50 , 000(0 . 20)+20 , 000(0 . 10) = 68 , 000. The wheat farmers expected profit is000....
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 Spring '11
 Probability

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