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SQQM3073 ACTUARIAL MATHEMATICS 2
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
to the expected, according to the assumed
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].
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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