$\mathbb{E}[aX + b] = a\mathbb{E}[X] + b$ (linearity) - $\mathbb{E}[X + Y] = \mathbb{E}[X] + \mathbb{E}[Y]$ (always, even if dependent) - $\mathbb{E}[XY] = \mathbb{E}[X]\mathbb{E}[Y]$ only if $X$ and $Y$ are independent