# Statistical sum of physical quantities in a quantum system

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. $\mathbb{E}[C^3] = a^3 + 3a^2\mathbb{E}[B] + 3a\mathbb{E}[B^2] + \mathbb{E}[B^3]$
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$\mathbb{E}[AB] = \mathbb{E}[A]\mathbb{E}[B]$ and your calculations are correct.