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Question for Krzys' from ASM Study Manual

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  • Question for Krzys' from ASM Study Manual

    Krzys'

    On page 23 of the manual, mid way, you have substituted u for x when rearranging the equation when working through the relationship of the hazard rate and the survival function.

    Should I take it that 0=<u=<x for the integral?

    Cheers,

    Miles
    Last edited by mallkins; January 6 2006, 09:53 PM.
    Proper prior planning prevents poor performance!

  • #2
    Originally posted by mallkins
    Krzys'
    On page 23 of the manual, mid way, you have substituted u for x when rearranging the equation when working through the relationship of the hazard rate and the survival function.
    Should I take it that 0=<u=<x for the integral?
    Cheers,
    Miles
    Yes. But I would not say that u is "substituted" for x. Rather, u is the variable used in integration, i.e., not an "active" variable.

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

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    • #3
      Thanks very much.

      Could the same also be said about t in the Moment generating function, where 1=<t=<n?

      Miles
      Last edited by mallkins; January 8 2006, 10:25 AM.
      Proper prior planning prevents poor performance!

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      • #4
        Mgf

        Originally posted by mallkins
        Thanks very much.
        Could the same also be said about t in the Moment generating function, where 1=<t=<n?
        Miles
        I am not quite sure what you mean. It is common to write t for the variable of the moment generating function. What is n?

        The issue of the variable used is not related to anything in probability, it comes from calculus: the variable used in the integrand should not be any of the variables used on the outside of the integral, as the variable under the integral is not an actual variable, just a notation for the integral. Once you go over advanced theory of integration you see that there is no need to write a variable: the integral is not of a variable, but of a function, and it is taken with respect not of a variable, but of a measure (in Lebesgue theory) or a division space/gauge (in Riemann-Henstock theory).

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

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