Numerical Random Variable/Expected Value

Uncertainty of a certain measurement

  • a numerical RV X labels events by values that are real numbers X.

  • the mean or expected value

E[X]=⟨X⟩=∑XX⋅P(x)\begin{gather*} \mathbb{E}[X]=\left\langle X \right\rangle=\sum_X X\cdot P(x) \end{gather*}

It is the probability of x occurring multiplied by the value of x.