Statistics - Table of Contents

X, Y · P(X = x) · f_X(x)

E[X] = Σ_x x P(X = x)
E[X] = ∫ x f_X(x) dx

E[Xⁿ]
Central: E[(X − μ)ⁿ]

Var(X) = E[(X − μ)²]
Var(X) = E[X²] − μ²

σ_X = √Var(X)

P(X = x, Y = y) · f_X,Y(x, y)

Discrete: P(X = x) = Σ_y P(X = x, Y = y)
Continuous: f_X(x) = ∫ f_X,Y(x, y) dy

P(Y = y | X = x) = P(X = x, Y = y) / P(X = x)
f_Y|X(y | x) = f_X,Y(x, y) / f_X(x)

Discrete: E[Y | X = x] = Σ_y y P(Y = y | X = x)
Continuous: E[Y | X = x] = ∫ y f_Y|X(y | x) dy

Cov(X, Y) = E[(X − μ_X)(Y − μ_Y)]
Cov(X, Y) = E[XY] − μ_X μ_Y

ρ_XY = Cov(X, Y) / (σ_X σ_Y) · ρ ∈ [−1, 1]