SearchOnMath

The normal density, \(p(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\), has become important in many applications because of its close relationship to the central limit theorem.

Euler's identity, \(e^{i\pi}+1=0\), relates the imaginary unit and two famous irrational numbers in a way that is so simple it has been called beautiful.

The total probability formula, \(P(A) = \sum_k P(A \cap B_k)\), relates the occurrence of an event \(A\) to that of several mutually exclusive events (\(B_k\)'s).