# Life expectancy expected value

Calculus Level 4

$f(x)=\frac{\pi}{14400}x\sin\left(\frac{\pi}{120}x\right),\ \ 0<x<120$

A life insurance actuary estimates probabilities of $$X$$, a person's life expectancy, with the probability density function as described above.

According to this model, what is $$\lfloor \text{E}[X]\rfloor$$?

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