(5) For a whole life insurance of 1,000 on (x) with benefits payable at the moment of death if it occurs within 10 years and 2,000 if it occurs after 10 years: (i) Z is the present-value random variable for the death benefits. (ii) Hx+t= 0.06 0≤t≤ 10 0.07 > 10 (iii) &, = { Calculate E(Z), E(Z²) and Var (Z). 0.04 0≤t≤ 10 0.05 > 10

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Actuarial Mathematics 1

(5) For a whole life insurance of 1,000 on (x) with benefits payable at the moment of death if it occurs
within 10 years and 2,000 if it occurs after 10 years:
(i) Z is the present-value random variable for the death benefits.
(ii) Hx+t=
0.06 0≤t≤ 10
0.07 t > 10
(iii) S₁ =
{
Calculate E(Z), E(Z²) and Var (Z).
0.04
0≤t ≤ 10
0.05 t > 10
Transcribed Image Text:(5) For a whole life insurance of 1,000 on (x) with benefits payable at the moment of death if it occurs within 10 years and 2,000 if it occurs after 10 years: (i) Z is the present-value random variable for the death benefits. (ii) Hx+t= 0.06 0≤t≤ 10 0.07 t > 10 (iii) S₁ = { Calculate E(Z), E(Z²) and Var (Z). 0.04 0≤t ≤ 10 0.05 t > 10
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