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

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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 ...
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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.

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