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Q&A Bank 1.30(ii)

Discussion in 'CT6' started by DMF, Jul 22, 2018.

  1. DMF

    DMF Member

    Hello,

    I am working through the solution to Q1.30(ii). Using the solution in part (i) the integral of [x . f(x)] between 100 and infinity is calculated. If x = infinity then am I right in thinking that the area under a normal distribution curve will = 1. Hence the 1 in the solution?

    Thanks!
     

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    DMF, Jul 22, 2018
    #1
  2. Colin Gray

    Colin Gray Member

    Hi DMF,

    As it happens, I'm working on the same question today. Yes, I think your understanding is correct but it would be good to hear this from one of the tutors/someone who has given it more thought.

    Related to this, I'd be grateful if someone could please confirm why the sigma^2 term disappears from the limits whenever a fixed value of X is used in the calculation (e.g. x = 100)? Is this because the value of 100 is a constant and so has no variance? See first couple of lines of calculations top of page 41 for example of sigma^2 being excluded from some of the calcs.

    Many thanks!
     
    Colin Gray, Jul 22, 2018
    #2
  3. John Lee

    John Lee ActEd Tutor Staff Member

    Yes, since \(ln \infty \rightarrow \infty \) (albeit very slowly) and \(\Phi(\infty)=1\).

    The \(\sigma ^2\) is not included in the terms for the second integral because \(k=0\).
     
    John Lee, Jul 23, 2018
    #3
  4. Colin Gray

    Colin Gray Member

    Great, I understand now. Thanks very much John.
     
    Colin Gray, Jul 25, 2018
    #4
    John Lee likes this.
  5. DMF

    DMF Member

    Thanks John, this helpful. I was getting distracted by the fact that it started at 100.
     
    DMF, Jul 27, 2018
    #5
    John Lee likes this.

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