| $p(A|B)=\frac{p(A\cap B)}{p(B)}$ |
$\Omega=\sum_{i=1}^n B_i , p(A)=\sum_{i=1}^n p(A\cup B_i)=\sum_{i=1}^np(A|B_i)p(B_i)$ |
| $A,B-indep<=>p(A\cap B)=p(A)p(B)$ |
$p(A|B)=\frac{p(B|A)p(A)}{p(B)}$ |
| $A,B-incop<=>p(A\cap B)=0$ |
$M(x)=\sum_{i=1}^n x_i p_i$ |
$F_\xi(x)=p(\xi<x)$ |
| $p(B_i|A)=\frac{p(A|B_i)p(B_i)}{\sum_{i=1}^n p(A|B_i)p(B_i)}$ |
$Var(x)=M(x^2)-M(x)^2$ |
$Cov(X,Y)=E\big[(X-EX)(Y-EY)\big]=E[XY]-(EX)(EY)$