stat430ps4

stat430ps4 - be drawn until one gets a cookie with at most...

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Homework 4, Statistics 430, Spring 2008 This homework is due Thursday, March 6 th . 1. a) Ross, Problem 4.41 in the Problems Section, page 192 b) What are the expected value and standard deviation for the number he gets correct if he did not have ESP? 2. Ross, Problem 4.42 in the Problems Section, page 193 3. Ross, Problem 4.53 in the Problems Section, page 194 4. Ross, Problem 4.56 in the Problems Section, page 194 5. Ross, Problem 4.60 in the Problems Section, page 194-195 6. Ross, Problem 4.72 in the Problems Section, page 196 7. The number of chocolate chips in a chocolate chip cookie is Poisson with a mean of 3. a) What is the probability that a cookie has at most one chocolate chip in it? b) In a bag of ten cookies, what is the probability that at most one cookie of the ten has at most one chocolate chip in it? c) What is the probability mass function for the number of cookies that would have to
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Unformatted text preview: be drawn until one gets a cookie with at most one chocolate chip in it? What are the mean and standard deviation of this random variable? d) A bag of cookies has 2 cookies with at most one chocolate chip and 8 cookies with more than one chocolate chip. If Sarah and Sam split the bag evenly (5 cookies each) at random, what is the probability that Sarah gets both cookies with at most one chocolate chip? 8. Show that the binomial probability mass function for given n and p is unimodal in x. Unimodal means that either p(x) decreases as x increases or p(x) first increases to to some maximum at a particular x, (call it x ) and then is non-increasing as x goes from x 0 to n. Hint: Consider p(x+1)/p(x) (see equation 6.3 in the text). When p(x+1)/p(x) 1 then p(x) is non-increasing from x to x+1 and when p(x+1)/p(x) >1 then p(x) is increasing from x to x+1....
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