Fundamentals of Probability Theory

• Events are subsets of the sample space that we can assign probability to
• The probability law of a random variable is defined as follows:

\[ \begin{align*}\mathbb{P}_X &: \mathcal{B}(\mathcal{R}) \to [0,1] \\ \mathbb{P}_X &= \mathbb{P} \circ X^{-1} \end{align*}\]