Results 1 to 4 of 4

Math Help - Independent Random Variables

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    9

    Independent Random Variables

    "Let X and Y be two independent random variables with the same probability density function given by

    f(x)= (
    e^(-x) if 0<x<inf.
    0 elsewhere
    )


    Show that g, the probability density function of X/Y, is given by

    g(t)=(
    1/(1+t)^2 if 0<t<inf.
    0 t<=inf.
    "


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DEUCSB View Post
    "Let X and Y be two independent random variables with the same probability density function given by

    f(x)= (
    e^(-x) if 0<x<inf.
    0 elsewhere
    )


    Show that g, the probability density function of X/Y, is given by

    g(t)=(
    1/(1+t)^2 if 0<t<inf.
    0 t<=inf.
    "


    Thanks!
    What have you tried? Where are you stuck?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    9
    I have found the density functions for both of x and y but dont know how to convert that to X/Y
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DEUCSB View Post
    I have found the density functions for both of x and y but dont know how to convert that to X/Y
    You were told the density functions. Have you done any research eg. Google the key words

    ratio distribution

    quotient random variables

    etc.

    What have you been taught in class regarding the algebra of random variables? eg. Change of variable theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sup of independent random variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 01:34 PM
  2. X,Y Random Variables, X+Y , 1 are independent?
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: October 1st 2009, 02:32 PM
  3. Independent Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 30th 2009, 02:03 PM
  4. independent random variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: January 26th 2009, 06:37 PM
  5. Independent Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: January 17th 2009, 12:24 PM

Search Tags


/mathhelpforum @mathhelpforum