Key Sequence Notation New Concepts Bernoulli distribution as an indicator conditional expectation law of total expectation Important Results / Claims Review: expectation. Expectation of the sums of random variables are linear regardless of whether or not the variables are IID, independent, whatever. “expectation of the sum is the sum of the expectations”. “Can I write the expectation I want to calculate as the sum of something else?” Questions Interesting Factoids \mathbb{E}[Y] = x=1: 3 x=2: 5 + Y x=3: 7 + Y \begin{equation} \mathbb{E}[Y] = 3 \cdot \frac{1}{3} + (5+ \mathbb{E}[Y]) \cdot \frac{1}{3} + (7+ \mathbb{E}[Y]) \cdot \frac{1}{3} \end{equation}