Question

5. You observed that the time your friend Alice talks on a phone conversation is exponentially distributed with mean 5 minutes. You call her one morning and her line is busy. Assuming that she is in a phone conversation: (a) (8.5 pts) What is the probability that she would finish the conversation in (b) (3 pts) What is the expected additional conservation time before she (c) (6 pts) If the conversation time is uniformly distributed with mean 5 another 5 minutes? finishes the call? minutes and you know that she has talked exactly 1 minute, what is the expected additional conversation time before she finishes the call?

Answer 1

here for exponential distribution ; parameter $\beta$ =5

a)

P(X<5) =1-e^-x/$\beta$ =1-e^-5/5 =0.6321

b)

expected additional time =$\beta$ =5 minutes

c)

E(X|X>1) =E(X|a=0,b=4)=(0+4)/2 =2.0 minutes