problemset39 - E ( X (1) ). b. Find the expected value of...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT/MA 416 December 7, 2011 Problem Set 39 Name: 1. Consider X 1 ,X 2 ,X 3 ,X 4 which are independent and uniformly distributed on [0 , 20]. a. Find the density of the first order statistic, i.e., find f X (1) ( x 1 ). b. Find the density of the second order statistic, i.e., find f X (2) ( x 2 ). 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2. Same setup as Question #1. a. Find the expected value of the first order statistic, i.e., find E ( X (1) ). b. Find the expected value of the second order statistic, i.e., find E ( X (2) ). 2
Background image of page 2
3. Let X 1 and X 2 be the waiting times for Alice and Bob until their respective phones ring. Assume that X 1 ,X 2 are independent exponentials, each with mean 10. a. Find the density of the first order statistic, X (1) , i.e., find f X (1) ( x 1 ). b. Find the density of the second order statistic, X (2) , i.e., find f X (2) ( x 2 ). 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
4. Same setup as Question #3. a. Find the expected value of the first order statistic, i.e., find
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E ( X (1) ). b. Find the expected value of the second order statistic, i.e., nd E ( X (2) ). 4 5. Let X 1 ,X 2 be independent, identically distributed, each with density f X ( x ) = 6( x-x 2 ) for 0 < x < 1, and f X ( x ) = 0 otherwise. a. Find the density of the rst order statistic, X (1) . b. Find the expected value of the rst order statistic, i.e., nd E ( X (1) ). 5 6. Design your own problem and solution. Create your own problem about order statistics. Design your problem in such a way that you would nd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
View Full Document

This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

Page1 / 6

problemset39 - E ( X (1) ). b. Find the expected value of...

This preview shows document pages 1 - 6. Sign up to view the full document.

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