# Formulas

(Difference between revisions)
 Revision as of 20:20, 24 April 2008 (view source)IvoDinov (Talk | contribs) (→Transformations)← Older edit Revision as of 20:24, 24 April 2008 (view source)IvoDinov (Talk | contribs) (→Transformations)Newer edit → Line 16: Line 16: * [[AP_Statistics_Curriculum_2007_Normal_Prob | Standard Normal to General Normal Transformation]]: $\mu+\sigma\times X$ * [[AP_Statistics_Curriculum_2007_Normal_Prob | Standard Normal to General Normal Transformation]]: $\mu+\sigma\times X$ * [[AP_Statistics_Curriculum_2007_Normal_Prob | General Normal to Standard Normal Transformation]]: $X-\mu \over \sigma$ * [[AP_Statistics_Curriculum_2007_Normal_Prob | General Normal to Standard Normal Transformation]]: $X-\mu \over \sigma$ - * [http://en.wikipedia.org/wiki/Normal_distribution Standard Normal to Chi Transformation]]: $|\ X |$ + * [http://en.wikipedia.org/wiki/Normal_distribution Standard Normal to Chi Transformation]: $|\ X |$ + * [http://en.wikipedia.org/wiki/Normal_distribution Standard Normal to Chi-Square Transformation]: $\sum_{k=1}^{\nu} X_k^2$

## Revision as of 20:24, 24 April 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: $f(x)= {e^{-x^2} \over \sqrt{2 \pi}}$
• General Normal PDF: $f(x)= {e^{{-(x-\mu)^2} \over 2\sigma^2} \over \sqrt{2 \pi\sigma^2}}$
• Chi-Square PDF: $\frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}\,$
• Gamma PDF: $x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!$
• Beta PDF: $\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1}\!$
• Student's T PDF: $\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}\!$
• Poisson PDF: $\frac{e^{-\lambda} \lambda^k}{k!}\!$
• Chi PDF: $\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}$
• Cauchy PDF: $\frac{1}{\pi\gamma \left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]}$