Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 207 / 1 / b / ii

Table of contents
- Solution ii

Solution

If

T

is future time to dementia from age 50, its survival function is

P (T > t) = {e^{- t /10}, e^{- 1} e^{- (t - 10) /5}, 0 \leq t \leq 10, t > 10.

The tail-sum formula for expectation gives the expected future time alive without dementia:

E T = \int_{0}^{10} e^{- t /10} d t + \int_{10}^{\infty} e^{- 1} e^{- (t - 10) /5} d t = 10 (1 - e^{- 1}) + 5 e^{- 1} = 10 - 5 e^{- 1} .

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version