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#41




September 17, 2005, exercise
Please find it at:
http://www.math.ilstu.edu/krzysio/9...OExercise.pdf I hope you will enjoy it. Yours, Krzys' 
#42




September 24, 2005, exercise
Please find it at:
http://www.math.ilstu.edu/krzysio/9...OExercise.pdf I hope you will enjoy it. Yours, Krzys' 
#43




October 1, 2005, exercise
Please find it at:
http://www.math.ilstu.edu/krzysio/10...OExercise.pdf I hope you will enjoy it. Yours, Krzys' 
#44




Krzys',
Good problem, but (IMO) not a good choice with only 24 days left before the exam. I'm not sure this is within the scope of Course 1/P (among the sample questions, the word "posterior" does not appear). While the strongest candidates should be able to follow the solution, under exam conditions this problem would separate the high 10's from the low 10's (and the lucky guessers from the unlucky guessers). Candidates, don't blame me if such a problem does appear and you didn't learn it. But I suspect for most of you, it would take a big effort to get comfortable with this idea, and you may have better uses for your limited remaining hours. If you think you know how to do it, by all means give it a try, and if you get it wrong figure out why. 
#45




Difficult problem
Dear Gandalph and everyone:
The last two problems I posted are very difficult, no doubt, and just on the boundary of what is listed in the syllabus. But I do believe that you will learn from them, either by doing them or just by reading the solutions. And, please note that there were previous posts on this forum that asked about almost exactly these two problems: I reworded the questions slightly, and wanted to make them more directly educational. The solutions posted previously on the forum were quite complicated  my intention was to help you by pointing out more direct approaches. Note also that I use the word "posterior" in the question, but also explain what I mean. The purpose is also to teach that this thing is called "posterior", but without that word the question indeed can be on the test. Note that the beta distribution is actually listed in the syllabus, let me quote: "Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chisquare, beta, Pareto, lognormal, gamma, Weibull, and normal)." This (undoubtedly painful) list has been a source of quite a lot of anxiety on this forum. My feeling is that a candidate should do as much as possible to become familiar with these distributions, so I intend to post problems that attack them from various angles. And by doing this problem, a candidate has a chance to go over the meaning of joint density, marginal density and conditional density  understanding of these concepts is a must for the exam. Finally, I believe that one should continuously increase the level of difficulty of things studied until two days before the test (the day before the test should be used for relaxation). Good luck on the test, everyone (not Gandalph, I understand that Gandalph is done with these trials of life and is not taking actuarial exams after having passed them  but that option is now available to Fellows, isn't it?). All the best. Yours, Krzys' Last edited by krzysio; 09242005 at 01:51 PM.. 
#46




Quote:

#47




the last two problems
Thanks Krzys' for the wonderful sample questions. Oct1 one is a very good practice question on beta distribution.
I figured out the last two problems, but I have some questions on it. Oct1: f(p)=p^2/3 is a pdf, should its integral over [0,1] be 1? Sept24: should answer C be 1/y2 instead of 1/y1? f(y1y2)=f(y1,y2)/f(y2)=2/2y2=1/y2. If I asked dumb questions, pls forgive me. I am getting dumb when the exam is close. 
#48




Answers to questions
Dear gppbb:
Shame on me, I was in a hurry to post some more problems before the test. Sorry ... I posted now corrected solutions, eliminating both the typos and calculation error. Very sorry. By the way, I changed the solution of the order statistics problem to make it more direct and intuitive, using only graphical representation  all bivariate uniform distribution problems really should be done this way. Yours, Krzys' Quote:

#49




Exercise for October 8, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/10...OExercise.pdf Please note that there has been a discussion on this forum on this kind of a problem. As you can see, I strongly advocate knowing the gamma function. I hope you will enjoy it. Yours, Krzys' 
#50




Exercise for October 15, 2005
Please find it at:
http://www.math.ilstu.edu/krzysio/10...OExercise.pdf It is meant to be very similar to a problem discussed at this forum and illustrates how you can do this kind of problem by taking the integral of the survival function. I hope you will enjoy it. Yours, Krzys' 
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examp, survival function 
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