Answers to 4B plus solution to 28

Stuart Klugman ( stuart.klugman@drake.edu )
Fri, 06 Nov 1998 08:24:21 -0600

The answers I get are
1-10: A,B,A,E,A,E,C,C,D,A
11-20: E,C,D,D,E,D,B,A,D,A
21:29: D,D,B,C,C,E,C,C,D

Here is my solution to number 28, I'd appreciate it if someone would check it out:

Let I(a,b) mean the integral from a to b of whatever follows.

The problem asks for I(50000,100000)xf(x)dx + 100000[1-F(100000)]
Rewrite as
I(0,100000)xf(x)dx + 100000[1-F(100000)] - I(0,50000)xf(x)dx
=E(X;100,000) - E(X;50000) + 50000[1-F(50000)]
=exp(10+.5)*Phi[(ln100000-10-1)/1]
+ 100000*[1-Phi[ln100000-10)/1]]
- exp(10+.5)*Phi[(ln50000-10-1)/1]
=36315.5*Phi(.5129) + 100000*[1-Phi(1.5129)] - 36315.5*Phi(-.1802)
=36315.5*.696 + 100000*.0652 - 36315.5*.4285
= 16234 which is answer C

------------------------------------------------------------------------------------------------
Stuart Klugman, FSA
Principal Financial Group Professor of Actuarial Science
Drake University
2507 University Avenue
Des Moines, IA 50311 USA
ph: 515-271-4097
e-mail: Stuart.Klugman@drake.edu