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# plugin-hw5 - CS206 HW5 Nov 6 2009 due in class Nov 25 or...

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CS206 HW5 Nov 6, 2009 (* due in class Nov 25, or before, at my office) (** is more challenging. You do not need to hand it in) 1. Do question 10 from HW4, now using the negative binomial random variable. 2. A fair die is tossed twice. Let Z be the sum of the tosses and W be the difference. Are Z and W independent? Explain. 3. (*) Find V ( Z ) in the above problem. 4. (*) Find the expected number of people getting their own hats in the 4 hat experiment. (Do this using (i) E ( X ) = w S X ( w ) P ( w ) and (ii) E ( X ) = a i Range ( X ) a i f X ( a i ).) 5. (*) Let X be the number of people who get their own hat in the 4 hat experiment. Find V ( X ), the variance. 6. (**) As above, but with the n hat experiment. 7. Similar to the question in the midterm, a student takes CS111, CS112, CS113, CS205, CS206, CS344, and in each receives a grade of F, D, C, C + , B, B + , A . The grade is given at random. Let N be the random variable that counts the number of distinct (i.e. different) grades he receives. Compute E ( N ) using the method of indicators.

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plugin-hw5 - CS206 HW5 Nov 6 2009 due in class Nov 25 or...

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