Need to prove that the following integral is positive

1. Jan 3, 2007

ardhu

I need help proving that the following (double) integral is positive:

int(limits from -infinity to +infinity) f(b) int(limits from b to +infinity) [e^{-(x-mean)/(2 *variance)}]/sq root(2 *pi *variance) dx db

thanks

Last edited: Jan 3, 2007
2. Jan 3, 2007

matt grime

This would be more appropriate elsewhere (calculus, say), but since exp is continous and always strictly positive it would entirely depend on what f is, and you've not stated that.

3. Jan 3, 2007

Staff: Mentor

I moved this thread to the Calculus homework forum, and deleted ardhu's duplicate thread in another forum. ardhu -- do not double-post, and please post homework questions in the appropriate homework forum. You also need to show your work so far in order for us to help you (Physics Forum rules).

4. Jan 3, 2007

ardhu

f is distributed normal. a quick update- i did calculate the inner integral in terms of the error function. and as the f is gaussian, i'm hoping that a closed form solution will emerge.i just need a clever way to prove that the net result is positive.

also this is not a homework problem.

5. Jan 3, 2007

Staff: Mentor

Fair enough, I'll take you at your word on that. I've moved the thread to the forum that matt suggested. Welcome to the PF, BTW.

6. Jan 3, 2007

matt grime

Everything in sight is a positive function, so the integral, if it exists, is positive. And the integral is easily shown to exist by some naive approximation (pretty much anything - it decays exponentially).