SOA Exam FAM Sample Question 2.2

Study guide: Exam FAM

Scientists are searching for a vaccine for a disease. You are given:

(i) 100,000 lives age $x$ are exposed to the disease

(ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1

(iii) The probability that the vaccine will be available is 0.2

(iv) For each life during year 1, $q_{x} = 0.02$

(v) For each life during year 2, $q_{x+1} = 0.01$ if the vaccine has been given, and $q_{x+1} = 0.02$ if it has not been given

Calculate the standard deviation of the number of survivors at the end of year 2.

[Question 20 on the Spring 2013 exam]

Concepts tested