ass1 - STAT455/855 Fall 2009 Applied Stochastic Processes...

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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT455/855 Fall 2009 Applied Stochastic Processes Assignment #1 Due Friday, Oct.2 Starred questions are for 855 students only. 1. Ross, Chapter 3 #28 (not in 8th edition). Polyas urn model supposes that an urn initially contains r red and b blue balls. At each stage a ball is randomly selected from the urn and is then returned along with m other balls of the same color. Let X k be the number of red balls drawn in the first k selections. (a) Find E [ X 1 ]. (b) Find E [ X 2 ]. (c) Find E [ X 3 ]. (d) Conjecture the value of E [ X k ], and then verify your conjecture by a conditioning argument. (e) Give an intuitive proof for your conjecture. Hint: Number the initial r red and b blue balls, so the urn contains one type i red ball, for each i = 1 ,...,r ; as well as one type j blue ball, for each j = 1 ,...,b . Now suppose that whenever a red ball is chosen it is returned along with m others of the same type, and similarly whenever a blue ball is chosen it is returned along with m others of the same type. Now, use a symmetry argument to determine the probability that anysame type....
View Full Document

Page1 / 2

ass1 - STAT455/855 Fall 2009 Applied Stochastic Processes...

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