Stat 470, Spring 2006

Homework Set 4, Due Friday 3/17/06 or Monday 3/27/06
====================================================


The reading for these problems is the rest of Chapter 2 
of the book-notes, but you might also want to look at the
portion of Chapter 3 on "Special integrals".

1. Suppose that a population of individuals aged 20 
has age at death T distributed so that T-20 ~ Weibull(5e-4,2).
(That is, the shape parameter gamma = 2 and the 
lambda parameter is 1/2000.)
(a) Find the expected age at death.
(b) Find the MEDIAN age at death, i.e., the age A 
such that  P(T > A) = 0.5 .

2. If a population has age at death distributed as
LogNormal(mu, sigma^2) with median age at death =60
and average age at death 75, find mu and sigma^2.
For this population, what is the probability of 
surviving past age 50 ? past age 82 ?

3. Suppose that a Makeham-Gompertz(A,B,c) distributed 
life distribution has median age at death 65, 
probability .75 of surviving past age 50, and 
probability .15 of surviving past age 80. Find A, B, 
and c, and calculate the probability for a life aged 
40 to survive to age 60.

In addition do problems (12), (14), and (16) at the end 
of Chapter 2.