SOA Exam ALTAM Sample Question 17
Study guide: Exam ALTAM
For (x) and (y) with independent future lifetimes, you are given that q_x = 0.2 and q_y = 0.1.
Part a (1 point)
Explain in words the meaning of the probability described by the symbol q_{xy}.
Part b (2 points)
You are also given that mortality within integral ages follows a uniform distribution of deaths assumption for each of (x) and (y) individually.
Sketch the graph of {}_sp_x as a function of s for 0 \le s \le 1. You should mark numerical values on each axis.
Part c (3 points)
Show that {}_sq_{xy} = s\,q_{xy} + g(s)\,q_{\overline{xy}} for 0 \le s \le 1, where g(s) is a function of s that you should specify.
(MLC, Fall 2014, Question 3)
Answer this question and see the worked solution