# Thread: Exponential distribution.

1. ## Exponential distribution.

a) Let X be the time until the next bus arrival. The time between two bus arrivals is
exponential with mean 10 minutes. You come to the bus stop and see a friend waiting. You ask
her how long she has been waiting, and she answers, 6 minutes. What is the expected time until
the bus arrival?
b) Now, suppose that bus arrivals happen deterministically every 10 minutes. How does your
answer change?

2. Originally Posted by sadasoria
a) Let X be the time until the next bus arrival. The time between two bus arrivals is
exponential with mean 10 minutes. You come to the bus stop and see a friend waiting. You ask
her how long she has been waiting, and she answers, 6 minutes. What is the expected time until
the bus arrival?
b) Now, suppose that bus arrivals happen deterministically every 10 minutes. How does your
answer change?
I don't know the answer for (a) without doing research, but I believe (b) gives expected wait time of 2 minutes; the next bus arrival is between 0 and 4 minutes from now and the probability is uniformly distributed.