linearity of expectation

Theorem

$\mathbb{E}[X+Y] = \mathbb{E}[X]+\mathbb{E}[Y]$

where $E[X]$ is expectation of $X$

Notes

• always true, no assumptions needed
• also applies to integral? when certain conditions apply (think of how expectation is an integral)

References:

1. https://www.chrismusco.com/amlds2023/notes/lecture01.html#Linearity_of_Expectation