General Case: The conditional expectation of exceeding a certain threshold
, given that the variable X has already survived to t, where t is the present time, is
Notes to the Chapter on Prophecy
Appendix to ANTIFRAGILITY by N.N. Taleb (of Amioun)
I wrote that a technology (book, cultural practice, religion) or any nonpresishable item is likely to increase in life expectancy upon mere aging --the opposite of perishable variables, like, say, humans.
General Case: The conditional expectation of exceeding a certain threshold , given that the variable X has already survived to t, where t is the present time, is
![(∫_X_t^∞X φ[X] X)/(∫_X_t^∞φ[X] X)](HTMLFiles/index_2.gif)
NONPERISHABLE Case: When X is power law distributed ( as I said with scalable matters) with exponent α, that is
P[x>X] = a 
then
E[X
]= 
, α>1
So when α =2, as is reasonable, the multiplier is 2. If technology is 10 years old, it can be expected to last another ten years. But that's not a big deal. We can see that the expectation lengthens with 
PERISHABLE CASE:Assume an exponential distribution:
f[x]=λ 
E[X
]=Xt+
The total life expectancy Xt does not change regardless of survival.
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