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  • Problem Solving Help

    I was trying to work through some problems in an old exam. Could someone help me out with these?

    The random variable X follows a two parameter Pareto distribution with parameters, theta = 100 and alpha = 2.
    The mean excess loss function, e_X(k) is defined to be E[X-k|X>=k].

    25. Determine the range of e_X(k) over its domain of [0,infinity).
    26. Y = 1.1X Determine the range of the function {e_Y(k)}/{e_X(k)} over its domain [0,infinity).
    27. Z = min(X,500) Determine the range of e_Z(k) over its domain of [0,500].
    Whether you are the lion or the gazelle, when the sun comes up, you better be running.

  • #2
    Originally posted by Ken
    I was trying to work through some problems in an old exam. Could someone help me out with these?

    The random variable X follows a two parameter Pareto distribution with parameters, theta = 100 and alpha = 2.
    The mean excess loss function, e_X(k) is defined to be E[X-k|X>=k].

    25. Determine the range of e_X(k) over its domain of [0,infinity).
    26. Y = 1.1X Determine the range of the function {e_Y(k)}/{e_X(k)} over its domain [0,infinity).
    27. Z = min(X,500) Determine the range of e_Z(k) over its domain of [0,500].
    If you use the fact that E[X-k|X>=k] = [E(X-k)] / [P(X>=k)], then you should be able to figure these out a little easier.

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    • #3
      Oh yeah, that makes more sense now.
      Whether you are the lion or the gazelle, when the sun comes up, you better be running.

      Comment


      • #4
        I figured wat would offer something helpful. Thank you for confirming.
        act justly. walk humbly. .

        Comment


        • #5
          Originally posted by .Godspeed.
          I figured wat would offer something helpful. Thank you for confirming.
          I only try.

          I'm sure I'll forget a lot of this stuff in a few weeks (unless, of course, Friday does not fall in my favor).

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          • #6
            I wish I could absorb everything you forget.
            Whether you are the lion or the gazelle, when the sun comes up, you better be running.

            Comment


            • #7
              Originally posted by Ken
              I wish I could absorb everything you forget.
              Indeed.

              Hey, wat, I'm "Searching." on AO, and somewhere I read you're in Hawaii. Two questions:

              1) If it's midnight EST, what time is it there? 7 PM?;

              2) How did you find an actuarial position in Hawaii? Maybe you lived there, but are there many there? Just curious.

              Thx.
              act justly. walk humbly. .

              Comment


              • #8
                Originally posted by .Godspeed.
                Indeed.

                Hey, wat, I'm "Searching." on AO, and somewhere I read you're in Hawaii. Two questions:

                1) If it's midnight EST, what time is it there? 7 PM?;

                2) How did you find an actuarial position in Hawaii? Maybe you lived there, but are there many there? Just curious.

                Thx.
                1) We're 6 hours behind. So I'm about to leave work pretty soon, while you're probably in bed.

                2) Born and raised. I was fortunate to catch a flyer at the math department of the university when I did. They took me on as an intern of sorts and I picked it up full-time. You're right in your inquisitive feelings, though - there aren't many positions out here. As far as I know, I think there are 2 actuarial programs in Hawaii, with a 3rd one possibly beginning (I think he's the only student). But, there are opportunities, as there are more than only two consulting agencies/insurance companies out here. But you'll have to make a case for them hiring you. There are some opportunities, but not too many.

                PM me for more details/ranting.

                Comment


                • #9
                  Originally posted by Ken
                  I wish I could absorb everything you forget.
                  I'm sure you'll do above and beyond how I performed on Exam M. Best of luck to you.

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