PX284 - A2 - continuous probability distributions

suppose is a continuous random variable with a probability, , of having a value between and

\int P (x) d x = 1

\begin{aligned} ⟨ x ⟩ & = \int x P (x) d x \\ ⟨ f (x) ⟩ & = \int f (x) P (x) d x \end{aligned}

σ_{x}^{2} = ⟨ x^{2} ⟩ - ⟨ x ⟩^{2}

σ_{x} = \sqrt{⟨ x^{2} ⟩ - ⟨ x ⟩^{2}}