According to 17th century data average life span was 26 years, however chance to live for no more than 8 years was 1/2. From that point estimate average life span of people, who have been living for not less than 8 years? Specify the range of possible values, considering only natural (non-decimal) numbers of years.
Note: Life span expected value. It is my first question about this task, in which I had explained my idea of solution, however recently I've found out, that everything was not as straightforward as it seemed to me at first, basically problem here is with years borders intersection, 8 years are being included in both intervals, so has impact on both expected values. And in this case I don't really know what to do.
Hint: try to calculate expected value for 8 years separately, and than you will get following ratio: $$26 \leq \frac{26-(\frac{1}{2}-r) \cdot q}{0.5+r} \leq 52$$ r - stands for probability to live up to exactly 8 years, try to find out what stands for q :). Then it is rather easy to retrieve answer out of mentioned inequality.