hw8_sol

# hw8_sol - IEOR 172 Probability and Risk Analysis for...

This preview shows pages 1–3. Sign up to view the full content.

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

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

Unformatted text preview: IEOR 172: Probability and Risk Analysis for Engineers, Fall 2007 Homework 8 Solution Chapter 5 Question 35 (a) exp h- R 50 40 λ ( t ) dt i = e- . 35 (b) e- 1 . 21 . Chapter 6 Question 6 The following gives an example only. To find the joint probability mass function, you need to calculate them for all possible values. P( N 1 = 2 ,N 2 = 2) = P(2nd and 4th are defective) = 2!2! 5! . Question 9 (a) Z 1 Z 2 f ( x,y ) dxdy = Z 1 Z 2 6 7 x 2 + xy 2 dxdy = Z 1 6 7 x 2 y + xy 2 4 ! | 2 dx = Z 1 6 7 2 x 2 + x dx = 6 7 2 x 3 3 + x 2 2 ! | 1 = 1 (b) f X ( x ) = 6 7 Z 2 x 2 + xy 2 dy = 6 7 (2 x 2 + x ) (c) P( X > Y ) = 6 7 Z 1 Z x x 2 + xy 2 dydx = 15 56 (d) P( Y > 1 / 2 | X < 1 / 2) = P( Y > 1 / 2 ,X < 1 / 2) P( X < 1 / 2) = R 2 1 / 2 R 1 / 2 x 2 + xy 2 dxdy R 1 / 2 (2 x 2 + x ) dx (e) E[ X ] = Z 1 x 6 7 (2 x 2 + x ) dx = 6 7 2 x 3 3 + x 2 2 ! | 1 = 5 7 1 (f) E[ X ] = Z 2 y 2 7 + 3 14 y dy = 1 7 y 2 + 1 14 y 3 | 2 = 8 7 Question 12 e- 5 + 5 e- 5 + 5 2 2!...
View Full Document

## This note was uploaded on 04/02/2008 for the course IEOR 172 taught by Professor Righter during the Fall '07 term at Berkeley.

### Page1 / 4

hw8_sol - IEOR 172 Probability and Risk Analysis for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online