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 the following problem. I need to consider all the conditions in which the following integral may be equal to zero:

$$\int_\Omega [p\phi-\lambda(\omega)]f(\omega)\iota(\omega)d\omega$$

Where $p>0$ is a constant. $f$ is a probability density function and $\iota$ is an indicator function (i.e I am truncating the density). $\lambda(\cdot)$ is an increasing function in $\omega$ and $\phi$ is a random variable, so I am solving this integral for any possible realization of $\phi$. Of course there is a trivial solution when $p\phi=\lambda(\omega*)$ for some $\omega*$. But there exist any other case when this is zero which I am not considering?

share|improve this question

1 Answer 1

  • The expectation $\mathbb{E}\left[\iota(p\phi-\lambda)\right]$ could be zero depending on the value of $p\phi-\lambda$ on all $\omega$.
  • If there is no $\omega$ for which $\iota(\omega)=1$, again you end up with a zero.
share|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.