assignment3solution

assignment3solution - 10/11 THE UNIVERSITY OF HONG KONG...

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

View Full Document Right Arrow Icon
10/11 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 3 Solution 1. (a) 4 3 (b) () < < + = 1 1 1 1 3 2 4 1 1 0 3 x x y y x x F (c) 0, 5 1 (d) 0.6575 (e) y y y f Y 4 1 3 = , 1 0 < y 2. (a) For , 10 > x () ( ) x t dt t x X P x F x x 10 1 10 10 0 1 10 2 = = = = Hence > = 10 0 10 10 1 x x x x F . (b) ( ) 3 2 15 10 1 1 15 1 15 = = = F X P (c) [] = = = × = 10 10 10 2 log 10 10 10 x dx x dx x x X E = = = × = 10 10 10 2 2 2 10 10 10 dx dx x x X E The random variable X does not have finite mean and finite variance. (d) [ ] 3246 . 6 10 20 20 10 10 10 2 1 10 2 3 10 2 = = = = × = x dx x dx x x X E (e) For any , 1 0 < < p p x p x p x F = = = 1 10 10 1. Therefore p p F = 1 10 1 , 1 0 < < p . Lower quartile: 3 40 25 . 0 1 10 25 . 0 1 25 . 0 = = = F x Median: 20 5 . 0 1 10 5 . 0 1 5 . 0 = = = F x Upper quartile: 40 75 . 0 1 10 75 . 0 1 75 . 0 = = = F x
Background image of page 1

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

View Full DocumentRight Arrow Icon
10/11 p. 2 ( ) (f) () 3 2 15 hours 15 least at for function can device a = = X P P Let Y be the number of devices out of 6 that can function for at least 15 hours. Then with the assumption of independence among the lifetimes, 3
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

Page1 / 5

assignment3solution - 10/11 THE UNIVERSITY OF HONG KONG...

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

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