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Probability Old Exam P Forum

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  #41  
Old 09-12-2005, 02:19 AM
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krzysio krzysio is offline
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Default September 17, 2005, exercise

Please find it at:
http://www.math.ilstu.edu/krzysio/9-...O-Exercise.pdf
I hope you will enjoy it.

Yours,
Krzys'
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  #42  
Old 09-23-2005, 04:25 AM
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Default September 24, 2005, exercise

Please find it at:
http://www.math.ilstu.edu/krzysio/9-...O-Exercise.pdf
I hope you will enjoy it.
Yours,
Krzys'
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  #43  
Old 09-24-2005, 02:37 AM
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Default October 1, 2005, exercise

Please find it at:
http://www.math.ilstu.edu/krzysio/10...O-Exercise.pdf
I hope you will enjoy it.
Yours,
Krzys'
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  #44  
Old 09-24-2005, 09:31 AM
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Default

Krzys',

Good problem, but (IMO) not a good choice with only 2-4 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.
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  #45  
Old 09-24-2005, 01:02 PM
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Default 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, chi-square, 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'
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Last edited by krzysio; 09-24-2005 at 01:51 PM..
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  #46  
Old 09-24-2005, 02:25 PM
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Quote:
Originally Posted by krzysio
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?).
If they made the option free, I might even try P and FM once each to see how I would do under pressure, even though the pressure wouldn't compare to the pressure on someone whose results mattered. At $165 and whatever FM costs, no way. Even free, I would probably come to my senses before spending the time.
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  #47  
Old 09-26-2005, 12:41 PM
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Default the last two problems

Thanks Krzys' for the wonderful sample questions. Oct-1 one is a very good practice question on beta distribution.
I figured out the last two problems, but I have some questions on it.
Oct-1: f(p)=p^2/3 is a pdf, should its integral over [0,1] be 1?
Sept-24: should answer C be 1/y2 instead of 1/y1? f(y1|y2)=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.
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  #48  
Old 09-28-2005, 12:20 AM
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Default 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:
Originally Posted by gppbb
Thanks Krzys' for the wonderful sample questions. Oct-1 one is a very good practice question on beta distribution.
I figured out the last two problems, but I have some questions on it.
Oct-1: f(p)=p^2/3 is a pdf, should its integral over [0,1] be 1?
Sept-24: should answer C be 1/y2 instead of 1/y1? f(y1|y2)=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.
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  #49  
Old 10-03-2005, 09:58 PM
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Default Exercise for October 8, 2005

It is posted at:
http://www.math.ilstu.edu/krzysio/10...O-Exercise.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'
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  #50  
Old 10-03-2005, 11:45 PM
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Default Exercise for October 15, 2005

Please find it at:
http://www.math.ilstu.edu/krzysio/10...O-Exercise.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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