# PS3s - (4) Answer: 0.26 P ( A ) = 0 . 18 , P ( B ) = 0 . 18...

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SOLUTIONS TO ISMT111 PROBLEM SET #3 (1) Answer: 0.9289. Pass Fail Training Course Training Course ( C ) ( C c ) Pass ( . 98 × 80) License Test ( L ) 78 . 4 6 84 . 4 Fail ( . 70 × 20) License Test ( L c ) 1 . 6 14 15 . 6 80 20 100 P (Pass Training Course | Passed License Test) = P ( C | L ) = 78 . 4 84 . 4 = 0 . 9289 . To use Bayes’ Formula: Given: P ( C ) = 0 . 80 , P ( L | C ) = 0 . 98 , so , P ( C c ) = 0 . 20 . P ( L c | C c ) = 0 . 70 , = P ( L | C c ) = 0 . 30 . P ( C | L ) = P ( C L ) P ( L ) = P ( L | C ) P ( C ) P ( L | C ) P ( C ) + P ( L | C c ) P ( C c ) = (0 . 98)(0 . 80) (0 . 98)(0 . 80) + (0 . 30)(0 . 20) (2) Answer: 0.11 A B ( . 15 × 60) ( . 05 × 40) Unsatisﬁed = 9 = 2 11 Satisﬁed 60 40 (3) Answer: (C) Stock C , since it has the highest median rate of return. Because P ( R B 25%) < 50% , P ( R A 25%) = 50% , P ( R C 25%) > 50% , the highest . (Sketch the three distributions: A is symmetric, B has a long tail to the right, whereas C has a long left tail.)

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Unformatted text preview: (4) Answer: 0.26 P ( A ) = 0 . 18 , P ( B ) = 0 . 18 , P ( A ∩ B ) = 0 . 05 , P (Either A or B but not both) = P ( A ∪ B )-P ( A ∩ B ) = P ( A ) + P ( B )-P ( A ∩ B )-P ( A ∩ B ) = 0 . 26 1 ATChan 2008 (5) Answer: (a) 0.24, (b) 0.2083 Default ( D ) Not Default ( D c ) Miss payment (1 . 00 × . 05) (0 . 20 × . 95) M . 05 . 19 0.24 Not Miss payment M c . 05 . 95 1 . 00 (a) P ( M ) = 0 . 05 + 0 . 19 = 0 . 24 (b) P ( D | M ) = 0 . 05 / . 24 = 0 . 2083 * * * 2 ATChan 2008...
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## This note was uploaded on 12/22/2009 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

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PS3s - (4) Answer: 0.26 P ( A ) = 0 . 18 , P ( B ) = 0 . 18...

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