Results 1 to 6 of 6

Math Help - Exponential transform

  1. #1
    Junior Member
    Joined
    Jul 2010
    Posts
    26

    Exponential transform

    If X and Y are Exp(1), we can write down that f(x+y) = exp -(x+y)

    Is it possible to verify this using the transformation:

    U = X+Y
    V = X-Y

    Any pointers most appreciated
    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 sharpe View Post
    If X and Y are Exp(1), we can write down that f(x+y) = exp -(x+y)

    Is it possible to verify this using the transformation:

    U = X+Y
    V = X-Y

    Any pointers most appreciated
    What you have posted doesn't make sense to me. Please post the original question exactly as it's stated. Is f(x + y) meant to be the joint pdf of X and Y? Or are you taling about the pdf of the random variable X + Y? Note: The sum of two exponential random variables is NOT what you are claiming.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2010
    Posts
    26
    Sure, the exact wording is:

    "If X,Y are i.i.d. Exp(1), write down the distribution of X+Y and verify this by use of this transformation U=X+Y, V=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 sharpe View Post
    Sure, the exact wording is:

    "If X,Y are i.i.d. Exp(1), write down the distribution of X+Y and verify this by use of this transformation U=X+Y, V=X-Y."
    Read 7.2 here: http://www.dartmouth.edu/~chance/tea...k/Chapter7.pdf

    For the verification part of the question, use the change of variable theorem (see for example Walpole, Myers and Myers (1998): Probability and Statistics for Engineers and Scientists, p 185).

    If you need more help, please show all your work and say where you get stuck.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2010
    Posts
    26
    thanks - that is really helpful. i will write again if I am stuck
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jul 2010
    Posts
    26
    Example 7.4 seems to give the answer I am looking for.

    My questions asks to verify by using U = X+Y and V=X-Y

    Example 7.4 gives the distribution function for U. I think I have worked out the distribution function for V also as

    f(v) = lamda/2 * (exp(-lamda *v) - exp(-3*lamda*v))

    Is it now a question of working out f(x) based on X=U+V?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The exponential and the Fourier transform.
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 15th 2011, 07:16 AM
  2. Replies: 3
    Last Post: April 22nd 2010, 05:39 AM
  3. Replies: 0
    Last Post: August 31st 2009, 02:02 AM
  4. Replies: 0
    Last Post: April 23rd 2009, 05:44 AM
  5. Replies: 2
    Last Post: February 23rd 2009, 05:54 AM

Search Tags


/mathhelpforum @mathhelpforum