solutions2

# solutions2 - Homework 2: Solutions Each such sequence has...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Homework 2: Solutions Each such sequence has probability quences. So the probability is and there are . which is a contradiction. . Hence, v j1 v QskS s i Therefore, . 1 p v 1 pv j1 S m v d 1 v QdlhS i b v 1 v Csi . (See Excercise 7.) Thus, . Now, v 1 f edi v 1 gf edi v v v Q %e 3. Chapter 2, Problem 8. We will use the fact that for any since i A3QscS "p which is a contradiction. If then , S ryp x v t i uQwu)srqp v v v #1 n q ro o i b lhS i b lhS v n Qsi hS m m S p Then there is a constant such that for all . If i 2. Chapter 2, Problem 6. Suppose there exists a that is uniform on then Y S b 2 dca ` X ' ( PIBF DB@ 8 ' QEHGECA9( P 7 &5 7 ' 6 6 RR4 (&&5 &%3 4 1 V T S b 2 hgUfeQ V T WUS v t Gu&u)si v v t AuQ&u)si v A3Qsi 2 the event that tosses are required. Then is in if and only if it is of the form such se- 1 0 ! ' %)(&&%\$# k3ejsihS v 1 i b v si v ! " that , exactly one of is and the rest are 1. Chapter 2, Problem 5. is the set of finite sequences such be . Let . hV h) Wh V k h V 4. Chapter 2, Problem 10. The only possible outcomes are V W% U Qw hS U%W%W) V V S By assumption T US u%h% H V u ) V u W)U h%WS H S V don't switch, you will win if or W) S V WWS ning is 1/3. If you switch, you win if or V W Q V probability of winning is 2/3. 5. Chapter 2, Problem 18. Use Bayes' theorem. 2 e ) 1 1 e ) 1 1 1 \$e so the probability of win. If you . . In this case, the ...
View Full Document

## This note was uploaded on 05/25/2008 for the course STAT 36-625 taught by Professor Larrywasserman during the Fall '02 term at Carnegie Mellon.

Ask a homework question - tutors are online