Practice Actuarial MLC Exam question For three fully discret

Practice Actuarial MLC Exam question.

For three fully discrete insurance products on the same (x), you are given:
(i) Z₁ is the present value random variable for a 20-year term insurance of 50.
(ii) Z₂ is the present value random variable for a 20-year deferred whole life insurance of 100.
(iii) Z₃ is the present value random variable for a whole life insurance of 100.
(iv) E[Z₁] = 1.65 and E[Z₂] = 10.75
(v) Var(Z₁) = 46.75 and Var(Z₂) = 50.78

Calculate Var(Z₃).

Solution

V(Z3)=V(Z1)+V(Z2)=46.75+50.78=97.53