# Formulas

(Difference between revisions)
 Revision as of 19:30, 24 April 2008 (view source)IvoDinov (Talk | contribs) (added Chi PDF)← Older edit Revision as of 19:32, 24 April 2008 (view source)IvoDinov (Talk | contribs) Newer edit → Line 1: Line 1: This [[Main_Page | 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 [http://socr.ucla.edu/htmls/SOCR_Distributome.html SOCR Distributome project] uses these formulas to represent PDFs, CDFs, transformations, etc. This [[Main_Page | 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 [http://socr.ucla.edu/htmls/SOCR_Distributome.html SOCR Distributome project] uses these formulas to represent PDFs, CDFs, transformations, etc. + + ==Probability Density Functions (PDFs)== * [[AP_Statistics_Curriculum_2007_Normal_Std |Standard Normal]] PDF: $f(x)= {e^{-x^2} \over \sqrt{2 \pi}}$ * [[AP_Statistics_Curriculum_2007_Normal_Std |Standard Normal]] PDF: $f(x)= {e^{-x^2} \over \sqrt{2 \pi}}$ Line 9: Line 11: * [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] PDF: $\frac{e^{-\lambda} \lambda^k}{k!}\!$ * [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] PDF: $\frac{e^{-\lambda} \lambda^k}{k!}\!$ * [http://en.wikipedia.org/wiki/Chi_distribution Chi] PDF: $\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}$ * [http://en.wikipedia.org/wiki/Chi_distribution Chi] PDF: $\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}$ + + ==Transformations== + * TBD + +

## Revision as of 19:32, 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: $\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}$

• TBD