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Weekly Practice Exam "P" Problems courtesy of Dr Krzysztof Ostaszewski

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  • Weekly Practice Exam "P" Problems courtesy of Dr Krzysztof Ostaszewski

    Thank you Dr. Krzysztof Ostaszewski for suggesting we post some of your sample problems. . Watch for further exam problems as he makes them available to us.
    Last edited by krzysio; August 4 2005, 11:26 AM. Reason: Name misspelled
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  • #2
    March 12th Problem

    http://www.math.ilstu.edu/krzysio/3-...O-Exercise.pdf
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    • #3
      March 19th Problem

      http://www.math.ilstu.edu/krzysio/3-...O-Exercise.pdf
      Last edited by admin; March 26 2005, 12:49 PM.
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      Email - [email protected]

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      • #4
        March 26th Problem

        http://www.math.ilstu.edu/krzysio/3-...O-Exercise.pdf
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        Email - [email protected]

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        • #5
          April 2nd Problem

          http://www.math.ilstu.edu/krzysio/4-2-5-KO-Exercise.pdf
          Actuary.com - www.actuary.com
          Email - [email protected]

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          • #6
            April 9 exercise

            Here is another practice problem:
            http://www.math.ilstu.edu/krzysio/4-9-5-KO-Exercise.pdf
            Yours,
            Krzys'
            Last edited by admin; April 4 2005, 09:59 AM.
            Want to know how to pass actuarial exams? Go to: smartURL.it/pass

            Comment


            • #7
              April 16 exercise

              http://www.math.ilstu.edu/krzysio/4-...O-Exercise.pdf
              Enjoy,
              Krzys'
              Want to know how to pass actuarial exams? Go to: smartURL.it/pass

              Comment


              • #8
                April 23 exercise

                Some discrete probability basics:
                http://www.math.ilstu.edu/krzysio/4-...O-Exercise.pdf
                Enjoy.
                Yours,
                Krzys'
                Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                Comment


                • #9
                  question about the 3-19-5 problem

                  I have a question about the 3-19-5 problem posted. In the 4th line of the solution:

                  Cov(X1-aX2-bX3,X2) = Cov(X2,X1) - aVar(X2) - bCov(X3,X2)

                  I'm not sure how you got from left hand side to the right hand side of the equation. I've never seen an covariance example like this. I'm familiar with the equation for the covariance of 2 variables, but not of the variance of an expression and a variable. Could you generalize the rule for me? Thanks very much.

                  Comment


                  • #10
                    Originally posted by engelbmj
                    I have a question about the 3-19-5 problem posted. In the 4th line of the solution:

                    Cov(X1-aX2-bX3,X2) = Cov(X2,X1) - aVar(X2) - bCov(X3,X2)

                    I'm not sure how you got from left hand side to the right hand side of the equation. I've never seen an covariance example like this. I'm familiar with the equation for the covariance of 2 variables, but not of the variance of an expression and a variable. Could you generalize the rule for me? Thanks very much.
                    I think you can think of covariance like an inner product, or, if you like, the FOIL method. So, in this case,
                    Cov(x1 - ax2 - bx3, x2)
                    = Cov(x1,x2) - Cov(ax2,x2) - Cov(bx3,x2)
                    = Cov(x1, x2) - a*Cov(x2,x2) - b*Cov(x3, x2)
                    = Cov(x1, x2) - a*Var(x2) - b*Cov(x3, x2)

                    Comment


                    • #11
                      Covariance

                      Wat is exactly right. Or look at it this way: Covariance is a linear operator in each of its variables (This problem's purpose was to teach you that, comes in handy in all covariance problems on the test)

                      Cov (X + Y, W) = Cov (X, W) + Cov (Y,W)
                      Cov (X, Y+W) = Cov (X, Y) + Cov (X,Y)
                      Cov (aX, W) =a Cov (X, W)
                      Cov (X, aW) =a Cov (X, W)

                      Does this help?

                      Yours,
                      Krzys'
                      Last edited by krzysio; April 17 2005, 02:21 AM.
                      Want to know how to pass actuarial exams? Go to: smartURL.it/pass

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                      • #12
                        April 30 exercise

                        http://www.math.ilstu.edu/krzysio/4-...O-Exercise.pdf
                        Enjoy!

                        Yours,
                        Krzys'
                        Last edited by krzysio; May 20 2009, 12:01 AM.
                        Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                        Comment


                        • #13
                          Weibull distribution

                          Yes, Weibull is on the test. And it is kind of hard to memorize all the distributions. So, to help you memorize the crucial item about the Weibull distribution, consider this exercise:

                          The time to failure X of an MP3 player follows a Weibull distribution. It is known that and that the probability that this player stil works after 3 years is 1/e, while the same probability for 5 years is 1/(exp(4)). Find the probability that this MP3 player is still functional after 4 years.

                          exp(4) means just e to the power 4.

                          In other words, what is the survival function of the Weibull distribution, and can you memorize it?

                          Yours,
                          Krzys'
                          Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                          Comment


                          • #14
                            Exercise for April 30, 2005

                            I have now posted this exercise with a solution:
                            http://www.math.ilstu.edu/krzysio/4-...O-Exercise.pdf
                            Enjoy.

                            Yours,
                            Krzys'
                            Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                            Comment


                            • #15
                              Exercise for May 7, 2005

                              I have now posted this exercise with a solution:
                              http://www.math.ilstu.edu/krzysio/5-7-5-KO-Exercise.pdf
                              Enjoy.

                              Yours,
                              Krzys'
                              Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                              Comment

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