Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $p(x)$ approximates the density of interest $q(x)$. Then $$\int f(x) q(x) = \int f(x) \left(\frac{q(x)}{p(x)} \right) p(x) \ dx = E_{p(x)} f(x) \left(\frac{q(x)}{p(x)} \right)$$

Why don't the $p(x)$'s cancel in the second equality?

share|cite|improve this question
The notation $E_{p(x)}$ is illogical, instead the RHS should read $E_p(fq/p)$. – Did May 5 '12 at 6:01

They do cancel in the middle phrase. In fact, that's how you know that the first statement is equal to the second statement. To get from the first to the second, they multiplied by $p(x)/p(x) = 1$, which doesn't change anything. They do this so that they can write it in the form of the last statement.

Without knowing the context, it's difficult to say more.

share|cite|improve this answer

Your Answer


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.