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

Answer:

Step-by-step 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%