Math Test

Bayes' Theorem

$$ \Pr (A\vert B)=\frac{\Pr (A)\times \Pr (B \vert A)}{\Pr (B)} = \frac{\Pr (A)\times \Pr (B \vert A)}{\Pr (A)\times \Pr (B \vert A) + \Pr (\neg A)\times \Pr (B \vert \neg A)} $$

Array

$$ \left[ \begin{array}{ccc} \lambda - a & -b & -c \
-d & \lambda - e & -f \
-g & -h & \lambda - i \end{array} \right] $$

Differential

$$ \iint xy^2,dx,dy =\frac{1}{6}x^2y^3, $$

Vector Problem

$$ u=\frac{-y}{x^2+y^2},,\quad v=\frac{x}{x^2+y^2},,\quad\text{and}\quad w=0,. $$