Probability law \(\mathbb{P}\)

• A probability law is a function \(\mathbb{P}:\mathcal{F} \rightarrow [0,1]\) of an event \(E\) to a real number in \([0,1]\)

• It is a measure of the size of a set. (Imagine it as the weight)

• Extends naturally to intervals \(E= [a,b]\) is a subset of \(\Omega = [0,1]\) for example and regions in higher dimensions.

\[ \mathbb{P}[E] = \int_a^b f(x) dx \text{ where f(x) is the 'weight' for x.} \]