Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have an expression of the form $$P(x) = \int_0^\infty \prod_{i=0}^{n} e^{-G(a, x_i)}\,\mathrm{d}a $$ and I was wondering if there was any way that I could swap the order of the product and the integral? I suspect not but its been a while since I had to manipulate integrals for myself. Ideally P(x) will represent the total probability of making i measurements from a Possion distributed system with zero occurences each time.

share|improve this question
    
In general, $\int fg \not= \int f \int g$. –  AlexE Jan 16 '12 at 10:51
    
Thanks, I thought that was probably the case. –  Bowler Jan 16 '12 at 11:43
    
1. I think you mean $\prod_{i=0}^N$?! 2. Would it help to write $e^{-\sum G }$? –  draks ... Jan 16 '12 at 13:29

1 Answer 1

up vote 2 down vote accepted

This is a CW answer intended to remove this question from the Unanswered queue.


As AlexE remarks, there is no general way to swap products and integrals.

This means that in general, evaluating integrals like the one stated can be quite hard, especially if the mapping $G$ is not in some way "nice".

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.