Formulas
From Socr
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* [http://en.wikipedia.org/wiki/Bernoulli_distribution Bernoulli to Binomial]: <math> \sum X_i </math> (iid) | * [http://en.wikipedia.org/wiki/Bernoulli_distribution Bernoulli to Binomial]: <math> \sum X_i </math> (iid) | ||
* [http://en.wikipedia.org/wiki/Bernoulli_distribution Binomial to Bernoulli]: <math> n = 1 </math> | * [http://en.wikipedia.org/wiki/Bernoulli_distribution Binomial to Bernoulli]: <math> n = 1 </math> | ||
+ | * [http://en.wikipedia.org/wiki/Binomial_distribution Binomial to Normal]: <math> \begin{vmatrix} \mu = np \\ \sigma^2 = np(1-p) \\n \rightarrow \infty \end{vmatrix} </math> | ||
+ | * [http://en.wikipedia.org/wiki/Binomial_distribution Binomial to Poisson]: <math> \begin{vmatrix}\mu = np \\ n \rightarrow \infty \end{vmatrix} </math> | ||
<hr> | <hr> |
Revision as of 08:58, 21 October 2008
This SOCR Wiki page contains a number of formulas, mathematical expressions and symbolic representations that are used in varieties of SOCR resources. Usage is defined as a reference by image, text, TeX, URL, etc. For instance the SOCR Distributome project uses these formulas to represent PDFs, CDFs, transformations, etc.
Probability Density Functions (PDFs)
- Standard Normal PDF:
- General Normal PDF:
- Chi-Square PDF:
- Gamma PDF:
- Beta PDF:
- Student's T PDF:
- Poisson PDF:
- Chi PDF:
- Cauchy PDF:
- Exponential PDF:
- F Distribution PDF:
- Bernoulli PMF: q = (1 − p) for k = 0,p for k = 1
- Binomial PMF:
Transformations
- Standard Normal to General Normal Transformation:
- General Normal to Standard Normal Transformation:
- Standard Normal to Chi Transformation:
- Standard Normal to Chi-Square Transformation:
- Gamma to General Normal Transformation:
- Gamma to Exponential Transformation: The special case of is equivalent to exponential Exp(λ).
- Gamma to Beta Transformation: .
- Student's T to Standard Normal Transformation:
- Student's T to Cauchy Transformation:
- Cauchy to General Cauchy Transformation:
- General Cauchy to Cauchy Transformation:
- Fisher's F to Student's T:
- Student's T to Fisher's F: X2
- Bernoulli to Binomial: (iid)
- Binomial to Bernoulli: n = 1
- Binomial to Normal:
- Binomial to Poisson:
- SOCR Home page: http://www.socr.ucla.edu
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