1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Transformation of the uniform distribution

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data

    I am told that X is a random variable with uniform distribution over [0,1]
    I need to find the mean and variance of log(X)

    2. The attempt at a solution
    I assume I must find the pdf of log(X) so I did this as follows;

    Let Y=log(X)
    Then to find the cumulative distribution function I considered;
    P(Y≤ y) = P(log(X)≤ y) = P( X < ey)

    I know that X is uniform over [0,1] so this is equal to
    ∫1.dy between ey and 0, where ey≤ 1

    This gives me that the cumulative distribution function = ey
    Which tells me that the probability density function is also ey

    Now what I am not sure of is what must y lie between, is this for y between eb and ea ?
  2. jcsd
  3. Nov 20, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    For X between 0 and 1, what is the range of log(X)?

    Anyway, to get the mean and variance of Y = log(X), you don't need the distribution of Y, although getting it is certainly one way of doing the problem.

  4. Nov 20, 2011 #3
    I think my lecturer wants me to do it this way. So y must be between - infinity and 0?
    Is my pdf correct now?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Transformation uniform distribution Date
Fourier transform of exponential function Thursday at 9:39 AM
Diffusion equation in polar coordinates Wednesday at 2:48 PM
Uniform distribution transform: e^2x Sep 15, 2011
Transforming a uniform distribution into a binomial May 22, 2011
Uniform Distribution Transformation Apr 28, 2011