oldfinal1 - UCSD ECE153 Prof. Young-Han Kim Handout #33...

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

View Full Document Right Arrow Icon
UCSD ECE153 Handout #33 Prof. Young-Han Kim Tuesday, June 1, 2010 Final Examination (Fall 2008) 1. Order statistics. Let X 1 ,X 2 ,X 3 be independent and uniformly drawn from the interval [0 , 1]. Let Y 1 be the smallest of X 1 ,X 2 ,X 3 , let Y 2 be the median (second smallest) of X 1 ,X 2 ,X 3 , and let Y 3 be the largest of X 1 ,X 2 ,X 3 . For example, if X 1 = . 3 ,X 2 = . 1 ,X 3 = . 7, then Y 1 = . 1 ,Y 2 = . 3 ,Y 3 = . 7. The random variables Y 1 ,Y 2 ,Y 3 are called the order statistics of X 1 ,X 2 ,X 3 . (a) What is the probability P { X 1 X 2 X 3 } ? (b) Find the pdf of Y 1 . (c) Find the pdf of Y 3 . (d) (Di±cult.) Find the pdf of Y 2 . (Hint: Y 2 y if and only if at least two among X 1 ,X 2 ,X 3 are y .) 2. Fair coins. We are given two coins: Coin 1 with bias (=probability of heads) 1 / 2 and Coin 2 with random bias P Unif[0 , 1]. We pick one at random and ²ip it three times independently. The value of the bias does not change during the sequence of tosses.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

oldfinal1 - UCSD ECE153 Prof. Young-Han Kim Handout #33...

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

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