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a4 - Math 4710 Homework 4 Due Friday Please remember that...

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Math 4710: Homework 4 Due Friday, September 26, 2008 Please remember that expressing your reasoning or proof clearly is very im- portant! You may discuss problems with other students but your writeups of homework must be your own. Homework is generally due in class or by class time under Dr. Back’s office door. Please read Chapter 5 in EPFA. The “extra problems” listed below are required to be handed in. We’ll use the term “extra credit” for problems you may but need not hand in. Joint Distributions Please hand in: problems 61, 62, and 66 in Section 3.5 of EPFA . Density Functions Please hand in: problems 1 and 4 in Section 5.6 of EPFA . Distribution Functions Please hand in: problems 6, 13, 15, 16, and 17 in Section 5.6 of EPFA . Please also look at problems 7, 8 and 14. Extra Problems 1. Let X n have a geometric distribution with p = λ n . Compute P ( X n n > x ) and show that as n → ∞ it converges to P ( Y > x ) where Y has an exponential distribution with parameter λ. 2. Data on the promotion records of 48 bank tellers (24 men and 24 women) is as given in the following table. Note that the table indicates that 35 of
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