Question

Two light bulbs, have exponential lifetime where expected lifetime for bulb A is 500 hours and expected lifetime for bulb B is 200 hours.

a) What is the expected time until bulb A or bulb B malfunctions ?

b) What is the probability that bulb A malfunctions before bulb B ?  

Answer 1

a)here parameter $\lambda$_A =1/500 and $\lambda$_B =1/200

a) expected time until bulb A or bulb B malfunctions=1/($\lambda$_A +$\lambda$_B ) =1/(1/500+1/200)=142.8571 Hours

b)

probability that bulb A malfunctions before bulb B =P(A<B)=$\lambda$_A/($\lambda$_A+$\lambda$_B)=(1/500)/(1/500+1/200)

=0.2857