Question

A disease has a constant force of mortality, µ. Historically 10% of all people with the disease die within 20 years. A more virulent strain of the disease is encountered with a constant force of mortality 2µ. What is the probability of an individual who has the new strain of the disease dying within 20 years?

Answer 1

Explanation:

For the disease having force of mortality µ.

we apply exponential distribution law

probability of dying within 20 years

p( x <20) =
`1-e^(-\mu)` = .1

`e^(-\mu)` = .9

For the disease having force of mortality 2µ.

we apply exponential distribution law

probability of dying within 20 years

p( x <20) = 1 -
`e^(-2\mu)`

= 1 - ( .9)²

= 1 - .81

= .19

or 19%