Question

The life time of a certain kind of battery is a random variable which has exponential distribution will mean of 200 hours. Find the probability that such a battery will i) last at most 100 hours i)last any where from 400 to 800 hours.

Answer 1

Mean =200 hours

$\lambda=\frac {1}{200}$

$f(x) =\int {\lambda e^{-\lambda x}} dx$

I) p(x<100)

$\int_0^{100} \frac {1}{200} e^{-\frac {1}{200}x}dx$

$-200* \frac {1}{200} e^{-\frac {1}{200}x}|_0^{100}$

=0.3935

ii) p(400<x<800)

$\int_{400}^{800} \frac {1}{200} e^{-\frac {1}{200}x}dx$

$-200* \frac {1}{200} e^{-\frac {1}{200}x}|_{400}^{800}$

=0.1170