Homework 1

# Homework 1 - (b Exactly one of the letters is in the right...

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Stat 116 Homework 1 Due Wednesday, April 9th. Please show work and justify answers. No credit for a ﬁnal answer with no explanation, even if the answer is correct. 1. We wish to form a 5 digit number using the digits 1, 2, . .., 9. The constraint is that none of the digits should be repeated more than twice . How many numbers can be formed respecting this constraint? 2. Ross (7th ed.) Page 17, problem 21 and Page 18,problem 22 3. Ross Page 55, problem 5 4. Ross Page 59, problem 33 5. Angry secretary problem. A secretary randomly mixed up 5 letters (i.e., putting them in the wrong envelopes.) You can think of each permutation of the 5 letters in the 5 envelopes as being equally likely. What is the probability that: (a) None of the letters end up in the right envelopes?
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Unformatted text preview: (b) Exactly one of the letters is in the right envelope? 6. Ross Page 62, problem 16 7. A couple has two children. What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl? (Assuming it is equally likely to have a boy or a girl.) 8. In any given year a male automobile policy holder will make a claim with probability p m , and a female policy holder will make a claim with probability p f , where p m 6 = p f . The fraction of the policyholders that are male is α , 0 ≤ α ≤ 1. A policyholder is randomly chosen. If A i denotes the event that this policyholder will make a claim in year i , show that P ( A 2 | A 1 ) > P ( A 1 ) 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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