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(Answered)-SQQM3073 ACTUARIAL MATHEMATICS 2 ASSIGNMENT 3 DATELINE: 11 MEI


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SQQM3073 ACTUARIAL MATHEMATICS 2

 

ASSIGNMENT 3

 

DATELINE: 11 MEI 2016

 


 

1. Suppose the cohort of example 5.2 (in lecture) is actually subject to a

 

uniform survival distribution on (0,15]. Compare the observed average

 

lifetimes

 


 

e^ 0

 


 

and

 


 

e^ 6

 


 

to the expected, according to the assumed

 


 

distribution.

 

2. A cohort of n persons is observed until all die, with deaths grouped in fixed

 

intervals. If Var [S(t) = 0.0009, Var [S(r)] = 0.0016, and their covariance is

 

Cov [S(t), S?] = 0.0008, find E[S(t)].

 

3. Assume that T is uniformly distributed over (t, t+1].

 

p.

 

a. Express (t*) in terms of t

 

^

 

b. Express the estimator ? (t*) in terms of the binomial random

 


 

variable Nt+1 (Note that this is conditional on nt being given.)

 

c. Find the approximate variance of (t*)

 

d. Is (t*) biased or unbiased?

 


 

 


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