Homework 2 - a third time to the same person and get the...

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Stat 116 Homework 2 Due Wednesday, April 18th. Please show work and justify answers. No credit for a Fnal answer with no explanation, even if the answer is correct. 1. Ross (7th ed.) Page 116, problem 49 2. Ross Page 125, problem 10 3. Ross Page 125, problem 11 4. Ross Page 125, problem 12 5. Ross Page 188, problem 14 6. Let { A k } n k =1 s.t. k A k = Ω and suppose P ( A k ) = p, k . (a) If at most 2 events can occur simultaneously prove p n - 1 . (b) Now additionally suppose P ( A i A j ) = q, i n = j what can be said about q ? 7. You are lost. Suppose two-thirds of the population are tourists and will give correct an- swers to questions about directions with probability 3/4. (assume answers to repeated questions are always independent) If you ask a non-tourist native the answer is always false. (a) You ask a passer-by whether you have to go East of West to get home. The answer is East. What is the probability this is correct? (b) You ask the same person again and get the same reply, what is the probability this is correct? (c) You ask for
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Unformatted text preview: a third time to the same person and get the same answer, what is the probability this is correct? (d) You ask for the fourth time and receive the answer East. Show that the probability it is correct is 27/70. (e) Show that had the fourth answer been West instead, the probability that East is nevertheless correct is 9/10. 8. Recall the previous problem. Tom is in the same position as you, but he has reason to believe that with probability ǫ East is the correct answer. Show that (a) whatever answer Frst received Tom continues to believe that East is correct with probability ǫ , (b) if the Frst two replies are the same (i.e. EE or WW) then Tom continues to believe that East is correct with probability ǫ , (c) after three like answers, Tom will calculate as follows P (East correct | EEE ) = 9 ǫ 11 − 2 ǫ , P (East correct | WWW ) = 11 ǫ 9 + 2 ǫ . 1...
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This note was uploaded on 01/13/2010 for the course STATS 116 taught by Professor Staff during the Spring '07 term at Stanford.

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