## (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

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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