Difference between revisions of "Formulas"
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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. | ||
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| + | ==Probability Density Functions (PDFs)== | ||
* [[AP_Statistics_Curriculum_2007_Normal_Std |Standard Normal]] PDF: <math>f(x)= {e^{-x^2} \over \sqrt{2 \pi}}</math> | * [[AP_Statistics_Curriculum_2007_Normal_Std |Standard Normal]] PDF: <math>f(x)= {e^{-x^2} \over \sqrt{2 \pi}}</math> | ||
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* [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] PDF: <math>\frac{e^{-\lambda} \lambda^k}{k!}\!</math> | * [[AP_Statistics_Curriculum_2007_Distrib_Poisson | Poisson]] PDF: <math>\frac{e^{-\lambda} \lambda^k}{k!}\!</math> | ||
* [http://en.wikipedia.org/wiki/Chi_distribution Chi] PDF: <math>\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}</math> | * [http://en.wikipedia.org/wiki/Chi_distribution Chi] PDF: <math>\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}</math> | ||
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| + | ==Transformations== | ||
| + | * TBD | ||
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| + | <hr> | ||
| + | * SOCR Home page: http://www.socr.ucla.edu | ||
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| + | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=Formulas}} | ||
Revision as of 14:38, 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\[\frac{2^{1-k/2}x^{k-1}e^{-x^2/2}}{\Gamma(k/2)}\]
Transformations
- TBD
- SOCR Home page: http://www.socr.ucla.edu
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