exercise_on_pro.ess_chp3-lastcbj

exercise_on_pro.ess_chp3-lastcbj - Printed April 16, 2009...

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

View Full Document Right Arrow Icon
Printed April 16, 2009 Exercise on Probability Essentials By Author. Jean Jacod, Philip Protter Byoung jin Choi e-mail: choibj@chungbuk.ac.kr Abstract In this book we solve a exercise of the Probability Essentials wrote by Jean Jacod, Philip Protter. Author thanks to graduate student of Department of Mathematics in Chungbuk National University in Republic of Korea. 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
1 Introduction 2 Axioms of probability 3 Conditional Probability and Independence Exercise 3.2 Suppose P ( C ) > 0 and A 1 , A 2 , ··· , A n are all pairwise disjoint. Show that P ( n n =1 A i | C ) = n X n =1 P ( A i | C ) . Proof. Since P ( n n =1 A i | C ) = P ( n n =1 A i C ) P ( C ) and P ( n n =1 A i C ) = P ( n n =1 ( A i C )) = n X n =1 P ( A i C ) . Hence this proof is completed. Exercise 3.6 Let ( A n ) n 1 ∈ A and ( B n ) n 1 ∈ A and A n A and B n B with P ( B ) > 0 and P ( B n ) > 0, all n . Show that (a) lim n →∞ P ( A n | B ) = P ( A | B ) (b) lim
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.

Page1 / 3

exercise_on_pro.ess_chp3-lastcbj - Printed April 16, 2009...

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