# HW6 - Section 3.3 19 Let j X be the weight(in lbs of the...

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Unformatted text preview: Section 3.3 19. Let j X be the weight (in lbs) of the j-th person, j = 1, 2, ..., 30. Hence, total weight is: 1 2 30 ... S X X X = + + + As j X ’s are independent with ( ) 150 j E X = and ( ) 55 j SD X = , we can use CLT to calculate: 5000 30 150 ( 5000) 1 0.0485 30 55 P S-- Φ = & 20. a) Investing \$100,000 in one stock gets the following distribution of the profit: k 20,000 10,000-10,000 P ( Profit = k ) 0.25 0.25 0.25 0.25 So (Profit 8,000) (Profit=10,000) (Profit=20,000) 0.5 P P P X = + = b) Let j X be the profit from the j-th investment. Let, 1 2 100 ... S X X X = + + + . By CLT, 8000 5000 ( 8,000) 1 0.0037 1118 P S- L = - Φ = & or considering continuity correction, the result is 0.0042. Section 3.4 1. a) 5 4 9 5 p q b) 6 q p c) 5 7 11 4 p q d) 5 5 8 5 2 13 2 8 5 8 5 k k k k k k k k p q p q p q k k k k--- = = = 2. Note that once the first ball is drawn all we do is to wait to see a ball of the other color. Hence, 1 D X = + , where X follows a geometric distribution with parameter ½. Hence, (...
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HW6 - Section 3.3 19 Let j X be the weight(in lbs of the...

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