hw6sol - SIEO 3658 Assignment #6 Solutions Probability...

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Unformatted text preview: SIEO 3658 Assignment #6 Solutions Probability November 5, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 3 Assignment #6 Solutions 1. A Cure for the Common Cold. By Bayes Rule, we get P [ Beneficial | T = 2] = P [ Beneficial ] P [ T = 2 | Beneficial ] P [ Beneficial ] P [ T = 2 | Beneficial ] + P [ not beneficial ] P [ T = 2 | not Beneficial ] = . 75 e- 3 3 2 / 2! . 75 e- 3 3 2 / 2! + 0 . 25 e- 5 5 2 / 2! = 0 . 8886 . 2. (a) Binomial(r, N, .25) (b) Binomial(r, N, .5) (c) P ( A | N = n ) = P ( N = n | A ) P ( A ) P ( N = n | A ) P ( A ) + P ( N = n | B ) P ( B ) = ( 100 n ) . 25 n . 75 100- n . 5 ( 100 n ) . 25 n . 75 100- n . 5 + ( 100 n ) . 5 n . 5 100- n . 5 = ( 100 n ) . 25 n . 75 100- n . 5 ( 100 n ) . 25 n . 75 100- n . 5 + ( 100 n ) . 5 100 . 5 (d) For n < 37 (e) Since P ( A | N = 40) = . 032, he labeled it type B. Therefore, P (He mislabeled the seeds) = P ( A | N = 40) = . 032 3. Let X i be the indicator random variable taking the value 1 or 0 depending on whether the first...
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hw6sol - SIEO 3658 Assignment #6 Solutions Probability...

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