7 A life insurance company models the mortality of an indivi

7. A life insurance company models the mortality of an individual as following a Gompertz law with hazard rate given by lambda = 0.00001ae^0.1t, where a is the frailty of the individual. It models a as following a gamma distribution with alpha = 0.4 and theta = 0.2. Calculate the probability that a randomly chosen individual lives to age 100.

Solution

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