Independence and correlations

📄️ The case of two events

We say that events $A, B \subseteq \Omega$ are independent if ${\mathbb P}[A \cap B] = {\mathbb P}[A] \cdot {\mathbb P}[B]$.

📄️ Multiple events

When we have more than two events, there can be many different degrees of independence.

📄️ Random graphs, revisited

Recall the Erdös-Rényi model of random graphs where we define the uniform probability space $(\Gamma_n, {\mathbb P})$.