$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$ $$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$$ $$\bar{x} = \frac{\sum x_i}{N}$$ $$Z = \frac{X - \mu}{\sigma}$$ $$R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$$ $$y = \beta_0 + \beta_1 x_1 + \epsilon$$ $$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$$ $$n=2025$$ $$p < 0.05$$ $$\beta_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$$ $$IQR = Q_3 - Q_1$$ $$E[\bar{X}] = \mu$$ $$\log(x)$$ $$2\pi r$$ $$N \sim (0,1)$$ $$H_0: \mu = 0$$ $$0.999$$ $$\text{Cov}(X,Y)$$ $$\text{Var}(X)$$ $$df = n-1$$ $$RMSE$$ $$MAE$$ $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ $$\lambda = 0.7$$ $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$ $$ANOVA$$ $$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$$ $$F = \frac{\text{Variance between groups}}{\text{Variance within groups}}$$ $$e^{i\pi} + 1 = 0$$ $$A \cap B$$ $$\sqrt{n}$$ $$Q_1, Q_2, Q_3$$ $$0.12345$$ $$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$ $$\sum_{i=1}^{N} x_i$$ $$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad-bc$$ $$\mathbb{E}[X]$$ $$\text{Binomial}(n,p)$$ $$\text{Normal}(\mu, \sigma^2)$$ $$n!$$ $$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$$ $$1.618$$ $$10^{5}$$ $$\pm \text{SE}$$ $$\alpha = 0.01$$ $$s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \bar{x})^2}$$ $$R = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$ $$A \cup B$$ $$X \sim \text{Poisson}(\lambda)$$ $$E = \sum x_i P(x_i)$$ $$N(p, q)$$ $$\Phi(z)$$ $$\delta^2$$ $$F-test$$ $$\text{Mode}$$ $$\text{Median}$$ $$s_p^2$$