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 Probability Old Exam P Forum

#111
07-02-2006, 02:30 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Pareto distribution

Quote:
 Originally Posted by SwingLH http://www.math.ilstu.edu/krzysio/4-2-5-KO-Exercise.pdf For this April 2 problem, I got answer D. 750. In fact, the Pareto expected value is 1000*3/(3-1)=1500. So the expected unconditional mean is 750. Did I miss anything?
Yes, you missed several things. The problem is about the Pareto distribution defined for x > 0, not for x > 1000 (in which case the survival function would be different). The version of the Pareto distribution defined for x > theta is generally not used on the actuarial exams, as losses can assume any nonnegative values. The solution shows you every step, so you can see that there is nothing wrong with it. As an exercise, you should derive the formula you are quoting, clearly stating its assumptions (you can follow the methodology in the solution of the problem I posted). The Pareto expected value is 1000/(3 - 1) = 500, not what you say, and what you give is the formula for the Pareto defined for x > 1000, and, of course 1500 = 500 + 1000. Are you using a textbook that does not show you all that? Are you sure you want to use it? In any case, you should n o t study the Pareto distribution defined for x > theta, you should study the one starting at zero.

All the best. Yours,
Krzys'
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#112
07-07-2006, 10:17 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Exercise for July 15, 2006

It is posted at:
http://www.math.ilstu.edu/krzysio/7-...O-Exercise.pdf
Yours,
Krzys' Ostaszewski

P.S. I will be an instructor in the SOA Course 7 seminar in Seattle, so I am posting some exercises early, for the time when I travel.
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#113
07-18-2006, 01:56 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Exercise for July 22, 2006

It is posted at:
http://www.math.ilstu.edu/krzysio/7-...O-Exercise.pdf
Yours,
Krzys' Ostaszewski
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#114
07-28-2006, 07:01 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Exercise for July 29, 2006

It is posted at
http://www.math.ilstu.edu/krzysio/7-...O-Exercise.pdf
Yours,
Krzys'
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#115
08-05-2006, 06:30 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Exercise for August 5, 2006

It is posted at
http://www.math.ilstu.edu/krzysio/8-5-6-KO-Exercise.pdf
Yours,
Krzys'
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#116
08-10-2006, 12:17 AM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Different approach

Quote:
 Originally Posted by michael solomon Dear Dr. Krzys' Ostaszewski, Thank you very much for postings these problems. They are a great help. The question from August 6, 2005 was: Let N1 and N2 be two independant poisson random variables with expected values 2 (for N1) and 3 (for N2). Find Var (N1 l N1 +N2 =5). Your answer is clear. However, first I tried writing all the combinations of N1 and N2 that total five (0,5)...(5,0), found the probabilty of this combination, found E(N1 l N1 + N2 = 5), E(N1^2 l N1 +N2 =5), and used Var = E(x^2) - E(x)^2. Should this approach work? I got the wrong answer. Whats wrong with this approach? Thank you again for all your hard work in helping with these problems.
There does not seem to be anything wrong with your approach, but you would have to make certain you have all probabilities correctly, and that you really calculate conditional probabilities, not unconditional ones.

Yours,
Krzys' Ostaszewski
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#117
08-12-2006, 12:51 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
August 12, 2006 problem

It is posted at:
http://www.math.ilstu.edu/krzysio/8-...O-Exercise.pdf
Good luck on the exam next week.
Yours,
Krzys' Ostaszewski
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#118
08-20-2006, 01:13 AM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
August 19, 2006 problem

It is posted at
http://www.math.ilstu.edu/krzysio/8-...O-Exercise.pdf
Yours,
Krzys'
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#119
08-20-2006, 01:18 AM
 Kazodev Member SOA Join Date: May 2004 Posts: 3,393

Quote:
 Originally Posted by krzysio It is posted at http://www.math.ilstu.edu/krzysio/8-...O-Exercise.pdf Yours, Krzys'
You have a typo? E(Y) = E(30X + 2X^2) = 30E(X) + 2E(X^2) not 3E(X^2)
#120
08-25-2006, 07:42 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,321
Exercise for August 26, 2006

It is posted at
http://www.math.ilstu.edu/krzysio/8-...O-Exercise.pdf
Yours,
Krzys'
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 Tags exam-p, survival function