5.8 Chapter 5 Formulas

Discrete Distribution Table: 0 ≤ P(x_i) ≤ 1 ∑ P(x_i) = 1	Discrete Distribution Mean: μ = Σ(x_i ∙ P(x_i))
Discrete Distribution Variance: σ² = ∑(x_i² ∙P(x_i)) – μ²	Discrete Distribution Standard Deviation: σ = $\sqrt{σ^{2}}$
Geometric Distribution: P(X = x) = p ∙ q ^{(x – 1)}, x = 1, 2, 3, …	Geometric Distribution Mean: μ = $\frac{1}{p}$ Variance: σ² = $\frac{1 - p}{p^{2}}$ Standard Deviation: σ = $\sqrt{\frac{1 - p}{p^{2}}}$
Binomial Distribution: P(X = x) = _nC_x·p^x ·q^(n-x), x = 0, 1, 2, …, n	Binomial Distribution Mean: μ = n ∙ p Variance: σ 2 = n ∙ p ∙ q Standard Deviation: σ = $\sqrt{n} \cdot p \cdot q$
Hypergeometric Distribution: P(X = x) = $\frac{a C_{x} \cdot_{b} C_{n - x}}{_{N} C_{n}}$	p = P(success) q = P(failure) = 1 – p n = sample size N = population size
Unit Change for Poisson Distribution: New μ = old μ( $\frac{new units}{old units}$ )	Poisson Distribution: P(X = x) = $\frac{e^{- μ} μ^{x}}{x!}$

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University), hosted on LibreTexts (stats.libretexts.org) and licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.