# Probability and statistics

```latex
P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}
```

```latex
\mathbb{E}[X]=\sum_x x\,P(X=x)
```

```latex
\operatorname{Var}(X)=\mathbb{E}\!\left[(X-\mu)^2\right]
```

```latex
f(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp\!\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)
```

```latex
\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i \qquad s^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2
```