{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Hmwk7Sol - ISyE 2027 Probability with Applications Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Solution to Homework 7 November 11, 2011 1. Solution: (a) 1% × 60% + 2% × 20% + 3% × 20% = 1.6%. (b) 3% × 20% 1.6% = 0.006 0.016 = 0.375. 2. Solution: (a)No. (b) 99% × 1 1000000 99% × 1 1000000 + 5% × ( 1- 1 1000000 ) = 1.98 × 10- 5 . (c) 99% × 1 10 99% × 1 10 + 5% × 9 10 = 0.6875. (d)No. The prior probability that a person is HIV positive is very low, just like person A, according to part (b), the probability that a person is HIV positive given the test is positive is very low. So it doesn’t make sense to use this test to do mass screenings of every resident in the state of Georgia. 3. Solution: (a) Y has the p.d.f f ( y ) = fl 1 + y , y < 1- y , y > So, h = 1. (b)Pr {- 1 2 < Y 6 1 2 } = R 1 2- 1 2 f ( y ) dy = 3 4 . (c)E [ Y ] = R 1- 1 yf ( y ) dy = R- 1 y ( 1 + y ) dy + R 1 y ( 1- y ) dy = 0. (e) Var ( Y ) = E [ Y 2 ]-( E [ Y ]) 2 = E [ Y 2 ] = R 1- 1 y 2 f ( y ) dy = R- 1 y 2 ( 1 + y ) dy + R 1 y 2 ( 1- y ) dy = 1 6 . (f)E [ Y- E [ Y ]] = E [ Y ] - E [ Y ] = 0....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

Hmwk7Sol - ISyE 2027 Probability with Applications Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online