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#81




Exercise for February 25, 2006
It is posted at:
http://www.math.ilstu.edu/krzysio/2...OExercise.pdf Yours, Krzys' Ostaszewski P.S. I will be an instructor in SOA Course 7 seminars in February and March, so I will be traveling. Also, Course P exam is next week. For these two reasons I thought it might be useful to post some more exercises now. I will post exercises for the rest of February and for March, as well as for April 1 now. Good luck on the exam and in all your studying. 
#87




For the April 1 problem, when you solved it you have that the answer is (2 * sigma^2)/n^2, which is choice D, but you put that the answer is E. I hope the answer is E, because that's what I got, otherwise I don't know what I did wrong.

#88




April 1 answer
My bad. Typo. The answer choice should be D. I posted a corrected version now.
But I also suspect your bad in the way you did it. Did you add the variances of differences in the step before the last one? You can't. They are not independent. You need to do what I did. Yours, Krzys' 
#89




It's those stupid mistakes that always seem to kill me on the practice problems. But I see what I did wrong. I saw the word independent and I assumed that the X's were independent. So I had
each Var [Xj] = Var [Zj  Zj1] = Var[Zj] + Var[Zj1] = 2 * (sigma)^2 So then I had 1/n^2 * Var[sum of all Xj] = 1/n^2 * (n * 2 * (sigma)^2) = (2 * (sigma)^2)/n But now I see that that's wrong because the Z's are independent and not the X's, and since the X's aren't independent, we can't just add the variances because we would also need to know the covariance between each of the X's. So now I understand how you got the answer. I just need to learn to read the questions more carefully before I answer them! 
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