1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Finding Expectation from the inverse CDF.

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data
    http://209.85.48.12/3560/8/upload/p2791776.jpg


    2. Relevant equations
    The most relevant identity to the part that I'm confused about is the following identity: for any cumulative distribution function F, with the inverse function F-1, if U has uniform (0,1) distribution, then F-1(U) has cdf F. Also useful: E(X) is the integral from -[tex]\infty[/tex] to [tex]\infty[/tex] of x * f(x), where f(x) = the probability distribution function of the distribution.


    3. The attempt at a solution
    The identity given for E(X) of a CDF makes perfect sense to me, and deducing the discrete corollary to the theorem makes sense too. Part C isn't anything I need help on, either; I've already used the formula to get it. But though I understand that these all make sense, I'm really just kind of confused about what they're asking in part A. What do they mean by using X=F-1(U) to show that E(X) can be interpreted as the shaded area above the CDF of X? Basically, what's the convention for integrating an inverse function representing a function that you don't know? I'm not looking for any coddling -- I'm just really rather confused by this problem and would like a push in the right direction to figure out what's up here.
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Apr 6, 2009 #2
    Not so much that point of view, but more like the reverse. The phrase "using X=F-1(U)" means use this change of variables to change the integral for E[X] into an integral in terms of F-1(u) and du.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding Expectation from the inverse CDF.
  1. Meaning of Inverse CDF (Replies: 0)

Loading...