Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Let $C = A + B$ (statistical sum, so $\mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]$), and let $p(A = a) = 1$. Are the following true?

  1. $\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$
  2. $\mathbb{E}[C^3] = a^3 + 3a^2\mathbb{E}[B] + 3a\mathbb{E}[B^2] + \mathbb{E}[B^3]$
share|improve this question
add comment

1 Answer

This is only true if A and B are independent. In that case,

$\mathbb{E}[AB] = \mathbb{E}[A]\mathbb{E}[B]$ and your calculations are correct.

Without knowing the distribution for B, this is the strongest supposition needed for your calculations to be correct.

share|improve this answer
4  
-1; Both identities are always true since A is non-random –  Slaviks May 8 '13 at 14:03
add comment

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.