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  • question on Exam P problem

    Hi folks,

    I was solving problems from the previous exams (downloaded from the SOA website). In that set of problems, I am little bit confused about Problem #112.

    According to the statement of the problem,

    domain for the joint density function, f(x,y) = 2(x+y), is all the region on the xy plain where f(x,y) is positive.

    That means, all the region to the "right" of the line y = -x on the xy plain. But then obviously it is an open region and double integral of f(x,y) over the entire region is not going to equal 1. In that case, f(x,y) is not a density function by definition. Also, x and y have to be positive. So that leave the first quadrant to be the region but again the problem remains.

    So how do you actually determine the region in that problem?

    Any help would be greatly appreciated.

    Thanks

  • #2
    Originally posted by SCIGEEK
    Hi folks,

    I was solving problems from the previous exams (downloaded from the SOA website). In that set of problems, I am little bit confused about Problem #112.

    According to the statement of the problem,

    domain for the joint density function, f(x,y) = 2(x+y), is all the region on the xy plain where f(x,y) is positive.

    That means, all the region to the "right" of the line y = -x on the xy plain. But then obviously it is an open region and double integral of f(x,y) over the entire region is not going to equal 1. In that case, f(x,y) is not a density function by definition. Also, x and y have to be positive. So that leave the first quadrant to be the region but again the problem remains.

    So how do you actually determine the region in that problem?

    Any help would be greatly appreciated.

    Thanks
    Read the question a bit more carefully. It says X and Y represent proportions, so by definition, they must each range from 0 to 1. It also says that one must purchase a basic policy before purchasing a supplemental. This suggests that the proportion of employees purchasing a basic policy, X, must be greater than the proportion of employees purchasing a basic policy, Y. So, from this information, our domain must be not just 0<X<1, 0<Y<1, but 0<Y<X<1.

    Does that help any?
    act justly. walk humbly. .

    Comment


    • #3
      Originally posted by .Godspeed.
      Read the question a bit more carefully. It says X and Y represent proportions, so by definition, they must each range from 0 to 1. It also says that one must purchase a basic policy before purchasing a supplemental. This suggests that the proportion of employees purchasing a basic policy, X, must be greater than the proportion of employees purchasing a basic policy, Y. So, from this information, our domain must be not just 0<X<1, 0<Y<1, but 0<Y<X<1.

      Does that help any?

      Absolutely. I somehow missed it while doing the problem.

      Thanks a lot .Godspeed.

      Comment


      • #4
        Originally posted by SCIGEEK
        Absolutely. I somehow missed it while doing the problem.

        Thanks a lot .Godspeed.
        No problem. Just never forget the basic rule: read, read, read the question. Can't stress this enough. I wish you the best on the test.

        When is the test again?
        act justly. walk humbly. .

        Comment


        • #5
          Originally posted by .Godspeed.
          No problem. Just never forget the basic rule: read, read, read the question. Can't stress this enough. I wish you the best on the test.

          When is the test again?
          Thanks.

          The test is next week.

          Comment


          • #6
            I signed up for the 22nd (as I have class on T and Th), though 21st and 23rd are possibilities also.

            Comment

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