Results 1 to 2 of 2

Math Help - uniform distribution

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    204

    uniform distribution

    Let X ~ U(0,1)
    Prove Y := \frac{-log(X)}{\lambda} has exponential distrution with parameter \lambda
    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 wik_chick88 View Post
    Let X ~ U(0,1)
    Prove Y := \frac{-log(X)}{\lambda} has exponential distrution with parameter \lambda
    This can be easily proved using the probability integral transform theorem:

    Suppose that Y is a continuous random variable with pdf f(y) and continuous cdf F(y). Suppose that X is a continuous standard uniform random variable. Then U = F^{-1}(x) is a random variable with the same probability distribution as Y. (For proof see for example Roussas G. G. (1997) A Course in Mathematical Statistics. Or just use a search engine).

    In your case, let Y be an exponential random variable with pdf f(y) = \lambda e^{-\lambda y}. Note: You will need to realise that If X ~ U(0, 1) then 1 - X ~ U(0, 1).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Mixing a uniform distribution with a normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 8th 2011, 09:27 AM
  2. Not the Uniform Distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 24th 2010, 09:24 PM
  3. Uniform Distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 23rd 2009, 09:38 PM
  4. uniform distribution / pdf
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 23rd 2009, 11:16 PM
  5. Another Uniform Distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 2nd 2007, 04:33 PM

Search Tags


/mathhelpforum @mathhelpforum