Results 1 to 2 of 2

Math Help - help with computing density of one variable change.

  1. #1
    Senior Member
    Joined
    Sep 2009
    Posts
    300

    help with computing density of one variable change.

    Let X~exponential(lambda).Let Y=X^.75. Compute the density of fy of Y.

    The answer to this is
    fY(y) = 4(lambda)(y^3)e^(-lambda*y^4) for y > 0 and equals 0 for y <= 0.

    My attempt:
    Y=x^0.75
    dx = 4dy / x^-0.75


    i then get

    integral from -inf to +inf of
    4(lambda)(y^3)e^(-lambda*y^4) dy


    from here i don't understand how to get to the answer
    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 Sneaky View Post
    Let X~exponential(lambda).Let Y=X^.75. Compute the density of fy of Y.

    The answer to this is
    fY(y) = 4(lambda)(y^3)e^(-lambda*y^4) for y > 0 and equals 0 for y <= 0.

    My attempt:
    Y=x^0.75
    dx = 4dy / x^-0.75


    i then get

    integral from -inf to +inf of
    4(lambda)(y^3)e^(-lambda*y^4) dy


    from here i don't understand how to get to the answer
    There are many ways of doing this. One simple way is to first get the cdf of Y:

    \displaystyle G(y) = \Pr(Y \leq y) = \Pr(X^{3/4} \leq y) = \Pr(X \leq y^{4/3}) = \int_0^{y^{4/3}} f(x) \, dx for y \geq 0 and zero otherwise.

    Then the pdf is given by \displaystyle g(y) = \frac{dG}{dy}. Using the chain rule and the Fundamental Theorem of calculus is a simple way of doing this.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 11th 2011, 06:06 AM
  2. Unusual random variable density function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 9th 2011, 08:57 PM
  3. Prove that f is the density function of a random variable Z?
    Posted in the Advanced Statistics Forum
    Replies: 9
    Last Post: April 13th 2010, 12:58 AM
  4. If two random variable have teh joint density
    Posted in the Statistics Forum
    Replies: 5
    Last Post: January 3rd 2010, 08:05 AM
  5. Continuous Random Variable and Density Function
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: November 2nd 2007, 06:57 AM

Search Tags


/mathhelpforum @mathhelpforum