Probability and Statistics with Mathematica and Excel
Mathematica:
Binomial: [tex]\binom{a}{b} \Rightarrow $Binomial$[n,m][/tex] Binomial
Average: [tex]\frac{1}{n} \cdot \sum_{i=1}^{n}x_i \Rightarrow $Mean$[\{x_1,x_2,\hdots,x_n\}][/tex] Mean
Median:[tex]\text{Median}[\{x_1,x_2,\hdots,x_n\}][/tex] Median
Modus: [tex]\text{Commonest}[\{x_1,x_2,\hdots,x_n\}][/tex] Commonest
Excel:
Binomial Distribution: [tex]P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{n-k} \Rightarrow $binomdist$(k$,$n$,$p$,true/false$) [/tex]
Poisson: [tex]P(X = k) = \frac{\mu^k}{k!}\cdot e^{-\mu} \Rightarrow $poisson$(\mu$,$k)[/tex]
Hypergeometric Distribution: [tex]P(X=k) = \frac{\binom{M}{k} \cdot \binom{N-M}{n-k}}{\binom{N}{n}} \Rightarrow $hypergeomdist$(k$,$M$,$N$,$n)[/tex]
Normal Distribution: [tex]\Phi_{\mu,\sigma}(x) = \Phi \left( \frac{x-\mu}{\sigma} \right) \Rightarrow $normdist$(x,\mu,\sigma,$true/false$)[/tex]
[tex]\Rightarrow $norminv$(P(X),0,1)[/tex]
Standard Deviation: [tex]\sigma := \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_i – \bar{x})^2} \Rightarrow $stdev$(x_1,x_2,\hdots,x_n)[/tex]
Experimental Standard Deviation: [tex]\sigma := \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i – \bar{x})^2} \Rightarrow $stdevp$(x_1,x_2,\hdots,x_n)[/tex]
Thomas Post on January 31st 2008 in Math with tags:excel, mathematica, probability, statistics