Formulas

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.

• 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\[\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}\!\]