| X, Y, Z | random variable; for noise variables, we use N, N_X, N_j, ... |
| x | value of a random variable X |
| P | probability measure |
| P_X | probability distribution of X |
| X_1, ..., X_n iid ∼ P_X | an i.i.d. sample of size n; sample index is usually i |
| P(Y|X = x) | conditional distribution of Y given X = x |
| P(Y|X) | collection of P(Y|X = x) for all x; for short: conditional of Y given X |
| p | density (either probability mass function or probability density function) |
| p_X | density of P_X |
| p(x) | density of P_X evaluated at the point x |
| p(y|x) | (conditional) density of P(Y|X = x) evaluated at y |
| E[X] | expectation of X |
| var[X] | variance of X |
| cov[X,Y] | covariance of X, Y |
| X ⊥⊥ Y | independence between random variables X and Y |
| X ⊥⊥ Y | Z | conditional independence |
| X = (X_1, ..., X_d) | random vector of length d; dimension index is usually j |
| C | structural causal model |
| P(Y_C; do(X := 3)) | intervention distribution |
| P(Y_C|Z = 2, X = 1; do(X := 3)) | counterfactual distribution |
| G | graph |
| PA_G(X), DE_G(X), AN_G(X) | parents, descendants, and ancestors of node X in graph G |