Results 1 to 3 of 3

Math Help - [SOLVED] P.D.F: Continuous random variables 2

  1. #1
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901

    [SOLVED] P.D.F: Continuous random variables 2

    Sorry, but I'm afraid I have two more problems.

    The following function represents queue time in minutes of people in a restaurant.

    f(x)=\frac{x}{2500}(100-x^2) for  <br />
0\leq x\leq 10
    x=0 otherwise

    a) What is the probability that a traveller will have to queue for more than 2 minutes? a:0.9216

    b) 3 people go independantly to the restaurant. Find the probability that one has to queue for less than one minute, another for between one and two minutes, and the third for more than two minutes.
    a:0.0064

    Any help is appreciated.
    I'm not sure where I need to integrate between, and the seond question just looks hideous.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I prefer my duck.

    (a)  {1\over 2500}\int_2^{10} x(100-x^2)dx

    (b) do we care which waits how long????
    because there are 3! rearrangements of this (multinomial)

    P(X<1)P(1<X<2)P(X>2)

    or 6P(X<1)P(1<X<2)P(X>2) if we don't care which person does what here

    where P(X<1)={1\over 2500}\int_0^{1} x(100-x^2)dx

    P(1<X<2)={1\over 2500}\int_1^{2} x(100-x^2)dx

    and P(X>2)={1\over 2500}\int_2^{10} x(100-x^2)dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901
    I like guard duck too. But thanks for the helpful response.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] P.D.F: Continuous random variables
    Posted in the Statistics Forum
    Replies: 4
    Last Post: March 15th 2010, 03:10 PM
  2. Replies: 6
    Last Post: November 15th 2009, 12:23 AM
  3. Continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 22nd 2009, 08:30 AM
  4. Continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 19th 2006, 12:02 AM
  5. continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 21st 2006, 12:00 PM

Search Tags


/mathhelpforum @mathhelpforum