A life insurer issues a last-to-die joint life policy to a couple. One is rated as uninsurable and is estimated to die in less than five years with a variance of two years. The other insured person is rated standard, is assumed to outlive the uninsured person, and is expected to die with a variance of 10 years. Assume that the deaths are independent. (This is rarely true due to broken heart syndrome and joint risk.) What is the variance of the total number of years that this couple survives?

Question

Gavyn Odonnell

Mathematics

17 August, 15:18

A life insurer issues a last-to-die joint life policy to a couple. One is rated as uninsurable and is estimated to die in less than five years with a variance of two years. The other insured person is rated standard, is assumed to outlive the uninsured person, and is expected to die with a variance of 10 years. Assume that the deaths are independent. (This is rarely true due to broken heart syndrome and joint risk.) What is the variance of the total number of years that this couple survives?

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Titan · Answer 1

12

Step-by-step explanation:

We will Let X to denote the number of years for which the first life survives; and

Y will denote the number of years for which the second life survives.

Being that we are given the following details about X and Y:

Var (X) = 2; Var (Y) = 10; X and Y are assumed independent.

Thus, the variance of the total number of years that this couple survives is given by:

Var (X+Y) = Var (X) + Var (Y) [The covariance term vanishes because X and Y are independent]

= 2 + 10

= 12