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 = $\sqrt {\sigma ^{2}}$
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( $\frac{\text { new units }}{\text { old units }}$ )	Poisson Distribution: P(X = x) = $\frac{e^{-\mu} \mu^{x}}{x !}$

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University, https://mostlyharmlessstat.wixsite.com/webpage), © Rachel Webb, licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.