Q&A Bank 1.30(ii)

[DMF]

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!

 

[Colin Gray]

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!

 

[John Lee]

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 \(k=0\).

 

[Colin Gray]

Great, I understand now. Thanks very much John.

 

[DMF]

Thanks John, this helpful. I was getting distracted by the fact that it started at 100.