Law of the unconscious statistician

The law of the unconscious statistician or LOTUS states the Expectation of a random function. In the discrete case,

𝔼 [𝑔 (𝑋)] = \sum 𝑥 \in s u p p (𝑋) 𝑔 (𝑥) ℙ (𝑋 = 𝑥)

and in the continuous case

𝔼 [𝑔 (𝑋)] = \int \infty - \infty 𝑔 (𝑥) 𝑑 ℙ (𝑋 = 𝑥) = \int \infty - \infty 𝑔 (𝑥) 𝑓 𝑋 (𝑥) 𝑑 𝑥

#state/develop | #lang/en | #SemBr