Results 1 to 2 of 2

Math Help - Much needed help on this integral/density function/probabilty world problem

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    canada
    Posts
    1

    Much needed help on this integral/density function/probabilty world problem

    Question:

    Fatima and Zack both have labs which end at noon. Every day after the lab they arrive at Satrbucks
    located on campus, independently. Zack arrives at time X and Fatima’s arrival time is Y, where X and Y are
    measuared in mintues afternoon. The indiviual density functions are:

    f1(x) =

    e^-x if x is greater or equal to 0,
    0 if x < 0

    f2(y) =

    (1/50)*y if 0 is less than or equal to y less than or equal to 10,
    0 if otherwise.

    (Zach arrives sometime after noon and is more likely to arrive promptly than late. Fatima always arrives by
    12:10 PM and is more likely to arrive late than promptly.) After Fatima arrives, she’ll wait for up to half an hour for
    Zack, but he won’t wait for her. Find the probability that they meet.



    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49

    Re: Much needed help on this integral/density function/probabilty world problem

    Simplest would be to get the density function for Zach arriving and bothering to stick around because Fatima is already there. At any moment between x=0 and x=10 the probability of that is e^(-x) (Zach arriving) times x^2/100 (Fatima already there). During the following 20 minutes, the second of these is one, instead. So evaluate the two definite integrals.

    Or form double integrals, e.g.,

    \int_0^{10} \int_0^x e^{-x}\ \frac{y}{50}\ dy\ dx

    ... where Fatima arriving first is the region under the line y=x.
    Last edited by tom@ballooncalculus; April 5th 2012 at 09:33 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Density function problem?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 20th 2011, 09:01 PM
  2. Probability Density Function needed
    Posted in the Advanced Statistics Forum
    Replies: 11
    Last Post: May 26th 2010, 05:24 AM
  3. Sine & Cosine Wave Function World Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2009, 03:02 AM
  4. Probabilty Density Function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 22nd 2008, 01:59 PM
  5. Probabilty forumla-quick help needed
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 30th 2008, 08:52 PM

Search Tags


/mathhelpforum @mathhelpforum