Life Expectancy

[Andy the Actuary]

Have a friend who is teaching probability and statistics and I mentioned to her that there was approximately a 50% chance that a person would live to life expectancy. She asked could I prove it. Being immersed in libation, nothing came to mind and I didn't care to reinvent a wheel. Can anyone point to a demonstration (e.g., society transactions, book on life contingencies) of this intuitive conclusion?

[rcline46]

The last time I played with the little qs and match to the life expectancy tables, I discovered that the tables were set for when 2/3 of the population was dead, that is, only a 33 1/3% chance of making it to life expectancy - this was back in the late 70's or so, and I still don't believe my results.

[tymesup]

Using the new 417e table, I get a life expectancy at age 1 of just under 82. At age 83, 56% of the cohort is still above ground.

At age 50, life expectancy = 34. At age 84, 53% of them are still breathing air.

At age 70, 16 years and 50% probability.