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Let $S_{0}(t) = (1-\frac{t}{105})^{1/5}$ be the survival function of a newborn. What is the median future lifetime at age $50$? So $$S_{50}(t) = \frac{S_{0}(50+t)}{S_{0}(50)} = \frac{\left(1-\frac{50+t}{105}\right)^{1/5}}{ \left(1-\frac{50}{105}\right)^{1/5}}$$

The median future lifetime would be the value of $s$ such that $$ \int_{0}^{s} \frac{\left(1-\frac{50+t}{105}\right)^{1/5}}{ \left(1-\frac{50}{105}\right)^{1/5}} \ dt = 0.5$$

Is that correct?

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    Are you looking for the _median_ or the _mean_?2012-07-20
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    @Sasha: Just by solving for it after doing the integration?2012-07-20
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    @Sasha: This would be correct for the probability density function, but not for the survival function.2012-07-20
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    @joriki Silly me. I have removed the incorrect comment.2012-07-20

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