The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Software » comp.soft-sys.matlab

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: pdf
Replies: 1   Last Post: Dec 5, 2012 12:39 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Roger Stafford

Posts: 5,929
Registered: 12/7/04
Re: pdf
Posted: Dec 5, 2012 12:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"george veropoulos" <> wrote in message <k9mrdr$35v$>...
> 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

u = G(x) = sqrt(x)

and the density would be

p(x) = dG(x)/dx * 1/(b-a) = 1/(2*sqrt(x)) * 1/3 = 1/(6*sqrt(x))

To verify this, take the integral of p(x) with respect to x from x = F(2) to x = F(5):

int(1/(6*sqrt(x)),'x',2^2,5^2) = 1/3*sqrt(5^2)-1/3*sqrt(2^2) = 1 ,

and indeed 1 is the value it should have.

Roger Stafford

Date Subject Author
Read pdf
george veropoulos
Read Re: pdf
Roger Stafford

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.