Thread: SOA sample #204
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Old 10-21-2018, 09:49 PM
gauchodelpaso's Avatar
gauchodelpaso gauchodelpaso is offline
Join Date: Feb 2012
College: Eastern Michigan U
Posts: 145

I found the easiest way for me to solve it was replacing x=1/2 right away, then the integral for all values of y is just the difference of 2 easy ones. I used the basic result of an Erlang that gives
(integral from 0 to infinite) (x^a * e^(-x/b) dx) = a! * b^(a+1)

Afterthought one year later: It's much simpler if the survival function is used: Pr(t>1/2) and at the end finding the complement. And when realizing that the integral Y*e-Y^dY is the expected value of an exponential with mean = 1.

Prelims: 1/P - 2/FM - 3F/MFE - LTAM - STAM
VEE: Economics - Corporate Finance - Applied Statistics

Last edited by gauchodelpaso; 09-10-2019 at 12:24 PM..
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