Need to prove that the following integral is positive

[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

 

[matt grime]

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

 

[berkeman]

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).

 

[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.

 

[berkeman]

also this is not a homework problem.

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.

 

[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).