Lesson 1: Joint Distributions

Understanding joint probability for multiple random variables.

Lesson 1: Joint Distributions

Joint Probability Mass Function

For two discrete random variables $X$ and $Y$, the joint PMF is: $P(X = x, Y = y) = p(x, y)$

Marginal Distributions

To find the distribution of just $X$ from the joint distribution, we sum over all possible values of $Y$: $p_X(x) = \sum_y p(x, y)$

Independence

Two random variables $X$ and $Y$ are independent if and only if: $p(x, y) = p_X(x) \cdot p_Y(y)$ for all $x$ and $y$.