The life span in hours of a battery is a random variable wit

The life span in hours of a battery is a random variable with the probability density function show below. Find the probability that the battery lasts more than 1000 hours. Report answer 4 decimal

F(x)= 1

Solution

given distribution function

F(X)=1-e^-x/500            X>0

A) we have to find probability that the battery lasts more than 1000 hours .

means P(X>1000)=?

then P(X>1000)=[F(x)]_{at infinity}-[F(x)]_at1000

                      =1-e^{-infinity/500}-1+e^-1000/500

                       =e^-2=0.1353

B) we have to find probability that the battery lasts no more than 500 hours.

means P(0<X<500)=?

so

P(0<X<500)=[F(x)]_{at 500} - [F(x)]_{at 0}

                  =1-e^-500/500-1+e^-0/500

                     =e⁰-e^-1

                    =1-0.3679=0.6321 answer