Question

A juicer works for T amount of time before it breaks, where T follows the exponential distribution with rate $\theta$ = 3. After sales service examines the juicer at times distributed according to a Poisson process with rate $\lambda$ = 2; if the juicer is found to be not working then it is immediately substituted.

1) Find the probability that a juicer is examined at least 2 times before it stops working.

2) Find the expected time between replacements of juicers.

Answer 1

O machine operates fore it fails, where I follows the exponentian distribution with rate o=3 o repair crew es the machine at times distributed a ecording to a sa Poission Poission process with rate dag. process won & the Let x denote wcachine the N Check repair crew Pol (n=a . k the x locachine P{x 72} ģeoga odbo 20 21 . = + - 0.67667 - 0.3233 by Herce T N exp (0 = 3) E (T) = oto e-ot at = o te de at = o 100 + 2-1 e-ot de OLO - 0 B Here o=3 E(T) = t be the expected time between replacements of machine