1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Multiple Random Variable Question

  1. Nov 10, 2013 #1
    1. The problem statement, all variables and given/known data
    A and B agree to meet at a certain place between 1 PM and 2 PM. Suppose they arrive at the meeting place independently and randomly during the hour. find the distribution of the length of time that A waits for B. (If B arrives before A, define A's waiting time as 0.)

    2. Relevant equations

    3. The attempt at a solution

    My professor provides the solutions to my homework questions, therefore, I have it but I do NOT understand. I'm working on finding the CDF of [itex]Z[/itex] BUT, since there are several approaches here goes the method of choice:

    [itex]X =[/itex]time of arrival for B
    [itex]Y =[/itex]time of arrival for A
    [itex]Z = X - Y[/itex] defines the waiting time for A with [itex]-1 <= x <= 1[/itex] and[itex]-1 <= y <= 1[/itex]

    now I just need [itex]F_Z(z)[/itex] and [itex]-1 <= z <= 1[/itex]

    I know I need to split up when [itex]-1 <= z <= 0[/itex] and [itex]0 < z <= 1[/itex]

    the first part
    [itex]F_Z(z) = \int_{1}^{2+z} \int_{{x-z}}^2 1 \,dy\,dx = (1/2)*(1+z)^2[/itex]

    However, the second part, my professor did something weird. My latex skills are horrible, so I just posted the picture.

    Now, I cannot understand why we wouldn't just do this : [itex]F_Z(z) = \int_{1}^{2-z} \int_{{y+z}}^2 1 \,dy\,dx = 1/2(1+z)^2[/itex]

    I am picturing a square over the coordinates [itex](1,1),(1,2),(2,1),(2,2)[/itex] and [itex]Z = X - Y[/itex] being a line going through it and intersecting [itex](1,1),(2,2)[/itex]. The upper part is where A doesn't wait and the lower half is where A does wait.

    I'm sorry for my horrible question asking skills.. Let me know if I need to provide more info! Thanks so much guys..

    Attached Files:

    Last edited: Nov 10, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted