5.8: Chapter 5 Formulas
- Page ID
- 26591
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Discrete Distribution Table: 0 ≤ P(xi) ≤ 1 ∑ P(xi) = 1 |
Discrete Distribution Mean: μ = Σ(xi ∙ P(xi)) |
| Discrete Distribution Variance: σ2 = ∑(xi2 ∙P(xi)) – 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) = nCx·px ·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) = \(\frac{e^{-\mu} \mu^{x}}{x !}\) |