Lecture 3

Lecture

The Conditional Expectation of $X$ given $Y$

$$\text{E}X\mid Y=y_i=\sum _i{x}_i\cdot P_{X\mid Y}(x_i\mid y_j)$$

The Law of Total Probability on Expectations is

$$\text{E}X=\sum _j\text{E}X\mid Y=y_i\cdot \mathbb{P}(Y=y_i)$$