hw4 - MATH 471 HW 4 Solutions Pengsheng Ji Office Hours:...

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Unformatted text preview: MATH 471 HW 4 Solutions Pengsheng Ji Office Hours: 4:05-5:05 PM Tuesday 5:20-6:20 PM Thursday 218 Mallot Hall 2.4.6 Let A=1 was received, B=1 was sent. Since they are received as sent with probability 0.9 but errors occur with probability 0.1, we have P ( A | B ) = 0 . 9 ,P ( A c | B ) = 0 . 1 ,P ( A c | B c ) = 0 . 9 ,P ( A | B c ) = 0 . 1 . Then P ( A B ) = P ( A | B ) P ( B ) = 0 . 9 * . 5 = 0 . 45 , P ( A B c ) = P ( A | B c ) P ( B c ) = 0 . 1 * . 5 = 0 . 05 . Hence, the probability that a 1 was sent given that we received a 1 is given by P ( B | A ) = P ( A B ) P ( A ) = . 45 . 45 + 0 . 05 = 0 . 9 . 2.4.17 Let A=the person voted, B 1 =a Conservative, B 2 =a Liberal, B 3 =an Independent. By the Bayes Formula, we have the probability she is Liberal given that she is a voter is given by P ( B 2 | A ) = P ( B 2 ) P ( A | B 2 ) 3 i =1 P ( B i ) P ( A | B i ) = . 5 * . 8 . 3 * 2 / 3 + 0 . 5 * . 8 + 0 . 2 * . 5 = 4 / 7 ....
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This note was uploaded on 09/22/2010 for the course MATH 413 at Cornell University (Engineering School).

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hw4 - MATH 471 HW 4 Solutions Pengsheng Ji Office Hours:...

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