Descriptive Statistics
$\bar{x} = \dfrac{\sum x_i}{n}$ $s = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n-1}}$
IQR $= Q_3 - Q_1$; outlier if $< Q_1 - 1.5\,\text{IQR}$ or $> Q_3 + 1.5\,\text{IQR}$
Probability
$P(A\mid B) = \dfrac{P(A \cap B)}{P(B)}$
Independent $\iff P(A\cap B)=P(A)P(B)$
Binomial: $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$
Geometric: $P(X=k)=(1-p)^{k-1}p$
Sampling Distributions
$SE_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}}$, $SE_{\hat p}=\sqrt{\dfrac{p(1-p)}{n}}$
Normal condition for $\hat p$: $np \ge 10$ and $n(1-p)\ge 10$
Inference (CI & Tests)
CI: statistic $\pm$ (critical value)(SE)
Test stat $=\dfrac{\text{statistic} - \text{parameter}}{SE}$
Two-sample: $SE=\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}$ (means), pooled $\hat p$ (proportions)
Chi-Square
$\chi^2 = \sum \dfrac{(O-E)^2}{E}$
GOF df $=k-1$; Independence/Homogeneity df $=(r-1)(c-1)$
Regression
$\hat y = b_0 + b_1 x$, residual $= y - \hat y$
$t = \dfrac{b_1}{SE_{b_1}}$, df $=n-2$