| symbol | latex code | explanation | |
|---|---|---|---|
P(A ∩ B) | P(A \cap B) | Probability of A and B occurring | |
P(A ∪ B) | P(A \cup B) | Probability of A or B occurring | |
P(A | B) | P(A \mid B) | Conditional probability of A given B | |
E(X) | E(X) | Expected value of random variable X | |
Var(X) | \text{Var}(X) | Variance of random variable X | |
Cov(X, Y) | \text{Cov}(X, Y) | Covariance of random variables X and Y | |
P(A) | P(A) | Probability of event A | |
P(¬A) | P(\neg A) | Probability of not A | |
P(A ∩ B) | P(A \cap B) | Probability of A and B | |
P(A ∪ B) | P(A \cup B) | Probability of A or B | |
P(A | B) | P(A \mid B) | Conditional probability of A given B | |
X | X | Random variable X | |
f_X(x) | f_X(x) | Probability density function of X | |
F_X(x) | F_X(x) | Cumulative distribution function of X | |
μ | \mu | Mean of a distribution | |
σ² | \sigma^2 | Variance of a distribution | |
σ | \sigma | Standard deviation of a distribution | |
Bin(n, p) | \text{Bin}(n, p) | Binomial distribution with n trials and probability p | |
Poisson(λ) | \text{Poisson}(\lambda) | Poisson distribution with rate λ | |
N(μ, σ²) | \mathcal{N}(\mu, \sigma^2) | Normal distribution with mean μ and variance σ² | |
Exp(λ) | \text{Exp}(\lambda) | Exponential distribution with rate λ | |
U(a, b) | \text{U}(a, b) | Uniform distribution on the interval [a, b] | |
E(X) | E(X) | Expected value of X | |
Var(X) | \text{Var}(X) | Variance of X | |
SD(X) | \text{SD}(X) | Standard deviation of X | |
Cov(X, Y) | \text{Cov}(X, Y) | Covariance of X and Y | |
Corr(X, Y) | \text{Corr}(X, Y) | Correlation of X and Y | |
H₀ | H_0 | Null hypothesis | |
H₁ | H_1 | Alternative hypothesis | |
α | \alpha | Significance level | |
p-value | \text{p-value} | Probability of observing the data under H₀ | |
z | z | Z-score in standard normal distribution | |
t | t | T-score in Student's t-distribution | |
H(X) | H(X) | Entropy of random variable X | |
I(X; Y) | I(X; Y) | Mutual information between X and Y | |
D(P || Q) | D(P \| Q) | Kullback–Leibler divergence between distributions P and Q | |
M_X(t) | M_X(t) | Moment generating function of random variable X | |
M_X(t) = E(e^(tX)) | M_X(t) = E(e^{tX}) | Definition of the moment generating function | |
M'(0) = E(X) | M'(0) = E(X) | The first derivative of the MGF gives the mean | |
M''(0) = Var(X) + (E(X))² | M''(0) = \text{Var}(X) + (E(X))^2 | The second derivative of the MGF relates to variance | |
P(X ≥ a) ≤ E(X)/a | P(X \geq a) \leq \frac{E(X)}{a} | Markov's inequality | |
P(|X − μ| ≥ kσ) ≤ 1/k² | P(|X - \mu| \geq k\sigma) \leq \frac{1}{k^2} | Chebyshev's inequality | |
P(Sₙ/n − μ ≥ ε) ≤ e^(−nε²/2σ²) | P\left(\frac{S_n}{n} - \mu \geq \epsilon\right) \leq e^{-\frac{n\epsilon^2}{2\sigma^2}} | Hoeffding's inequality for large deviations | |
P(A | B) | P(A \mid B) | Posterior probability of A given B | |
P(A | B) = (P(B | A)P(A)) / P(B) | P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)} | Bayes' theorem | |
P(A, B) | P(A, B) | Joint probability of A and B | |
P(A ∩ B) = P(A)P(B | A) | P(A \cap B) = P(A) P(B \mid A) | Chain rule of probability | |
Y = β₀ + β₁X + ε | Y = \beta_0 + \beta_1 X + \epsilon | Linear regression equation | |
R² | R^2 | Coefficient of determination | |
ρ(X, Y) | \rho(X, Y) | Pearson correlation coefficient between X and Y | |
Cov(X, Y) = E(XY) − E(X)E(Y) | \text{Cov}(X, Y) = E(XY) - E(X)E(Y) | Covariance formula |