
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 23rd, 2016, 06:58 AM  #1 
Newbie Joined: Dec 2016 From: US Posts: 6 Thanks: 0  Waiting time for n buses (pdf)
In order to go from city A to city B you have to take n buses. For each of them you have to wait at the bus stop some time $\displaystyle \tau_{i}, i=1,2,...,n$. In each case, the probability that a bus arrives in a time interval $\displaystyle [t, t + dt)$ is equal to $\displaystyle rdt$, independently for each interval of time. Let T be the total time you have to wait for buses. What is the probability density function (pdf) of T?
Last edited by mike22; December 23rd, 2016 at 07:01 AM. 
December 23rd, 2016, 01:44 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,343 Thanks: 534 
The density function for each stop is $\displaystyle re^{rt}$. To get the density function for the sum of the weight times, you can use the characteristic functions (Fourier transform of the density). Since the weight times all have the density, get the nth power of the characteristic function and then take the inverse transform to get the density function of the sum.


Tags 
bus, buses, pdf, time, waiting 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Waiting time for n bus (pdf)  mike22  Probability and Statistics  0  December 23rd, 2016 06:57 AM 
waiting for help, solving the problem;  Shabir Kathio  Calculus  1  April 21st, 2015 12:02 AM 
Compute the average waiting time  faustinef  Advanced Statistics  0  December 4th, 2013 03:11 AM 
Waiting time vs Deadline equation  carlmazz  Computer Science  0  March 3rd, 2013 03:42 PM 
The waiting boy problem  takatoo  Advanced Statistics  7  July 31st, 2009 07:01 AM 