Question

Problem 4. The life X, in hours, of a certain device, has a pdf 100 , t 100 0, t< 100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.

Answer 1

a)probability that device will survive 150 years =P(T>150)=$\int_{150}^{\infty }$ f(t) dt =$\int_{150}^{\infty }$ 100/t² dt =-100/t |^$\infty$₁₅₀

=100/150=2/3 =0.6667

b)

expectancy =E(t)=$\int_{100}^{\infty }$ t*f(t) dt =$\int_{100}^{\infty }$ 100/t dt= 100*ln(t) |^$\infty$₁₀₀ =100*ln($\infty$)-100*ln(100) ~$\infty$

as ln($\infty$) tends to infinite ; therefore life expectancy of the device does nt exist. or infinite