I've been given the following question which was part of a past exam paper.
Q3) Trains arrive at a station at the rate of 25 per hour.
a) What is the probability that the time between trains arriving is 6 minutes or less?
I have attempted this question again, following some of the formulae which I found in some of the links given to me.
I apologise if this isn't the typical way of demonstrating workings, I will reformat if needs be.
b) The train company wants to state that waiting times (in minutes) between trains have been targeted for improvement. It fails to meet its target 40% of the time. What target has it set itself?
For this part, this is what I've got so far:
P(Xt<x)=0.6
, since they are succeeding in having a train arrive within this time 60% of the time, which means 0.6=1-e^-0.4167x
but I think I've gone wrong again as this is giving me the answer that x=-1.23
which can't be right because . Not sure where to go from here.
c) A train enthusiast notes that a goods train arrives, on average, once an hour. What is the probability that two goods trains will arrive in one hour?
Not sure how to approach this one.
d) If the enthusiast wishes to stay at the station for an hour, what is the probability that he will see at least one goods train in that time?
Not sure how to approach this one.
I've been in correspondence with my lecturer and she says this is a pretty straightforward problem. I know you're not meant to provide exact solutions to problems and just guide me to the answers myself, but I can't help but think I'm missing something really obvious which is making this hard for me.
It's worth noting that we've not been given anything about exponential probability distribution functions in our textbooks etc so I don't know if there's some other way of getting the answers I need.
Any help appreciated.
self-study
tag and read its wiki, which includes guidelines for asking self-study questions. One such guideline is to show that you have made a "good faith" attempt to solve the problem yourself and show us where you are stuck. Questions that do not show a good faith attempt may be subject to closure. $\endgroup$