# Conditional expectations

0 votes
53 views
asked Nov 9, 2017

In the above paper, for Question 5, the memo uses the following statement.

$$E[v^{K_{60}+1}|K_{60}\ge 10]=E[V^{K_{70}+11}]$$

I was under the belief that we are only allowed to drop the conditional part of an expectation if the random variables were independent. i.e. $$K_{60}$$ and $$K_{70}$$ were independent. However, surely $$K_{60}$$ and $$K_{70}$$ are not independent?

## 1 Answer

0 votes
answered Nov 14, 2017 by (720 points)
You are not really dropping the conditional expectation. You should think of it as a re-parametrization. Given that the curtate future lifetime of the life aged 60 is greater than or equal to 10, we are just reparametrizing the life to be aged 70.