"george veropoulos" <firstname.lastname@example.org> wrote in message <email@example.com>... > I have a variable ? tha is function of randon variable ? (?=F(?), F is a complex > function !) > (the variable ? is uniformly distributed in the interval [-? ?]) > ?y question is who i cant find the distribution of ? variable . - - - - - - - - - - The text of your message did not come through very well, George. I am guessing that you have a (complicated) function x = F(u) where u is a random variable uniformly distributed on the interval [a,b], and you wish to know the probability density of x over its corresponding span. Is that correct?
If we assume F is monotone increasing, then its inverse would be a function G where u = G(x). The probability density would then be:
p(x) = dG(x)/dx * 1/(b-a) .
This means that you have to be able to find the derivative of the inverse of F.
As an example, suppose x = F(u) = u^2 and [a,b] = [2,5]. Then the inverse function would be