Deferred mortality probabilities

In this exercise, you will help Cynthia to better understand the concept of a $k$-year deferred mortality probability for an 18-year-old. This is the probability that one first survives $k$ years, reaches age $18+k$ and then dies in the next year:

$$ \begin{aligned} {}_{k|}q_{18} &= {}_kp_{18} \cdot q_{18+k}. \end{aligned} $$ These probabilities with $k = 0, 1, 2, \ldots$ determine a discrete probability distribution. They run over all possible ages at death for the 18-year-old and express the corresponding probability to die at each of these ages.

The mortality rates $q_x$ and the one-year survival probabilities $p_x$ have been preloaded as qx and px.

Define kpx as the survival probabilities ${}_kp_{18}$ of an 18-year-old for $k = 0, 1, 2, \ldots$
Assign the deferred mortality probabilities ${}_{k|}q_{18}$ to the variable kqx by multiplying kpx with the mortality rates qx from 18 + 1 until length(px).
Compute the sum() of kqx to verify that it equals one.
Visualize the kqx against 0:(length(kqx) - 1).

Exercise

Deferred mortality probabilities

Instructions