Probability and Statistics with Mathematica and Excel

Mathematica:
Binomial: \binom{a}{b} \Rightarrow $Binomial$[n,m] Binomial

Average: \frac{1}{n} \cdot \sum_{i=1}^{n}x_i \Rightarrow $Mean$[\{x_1,x_2,\hdots,x_n\}] Mean

Median:\text{Median}[\{x_1,x_2,\hdots,x_n\}] Median

Modus: \text{Commonest}[\{x_1,x_2,\hdots,x_n\}] Commonest

Excel:
Binomial Distribution: P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{n-k} \Rightarrow $binomdist$(k$,$n$,$p$,true/false$)

Poisson: P(X = k) = \frac{\mu^k}{k!}\cdot e^{-\mu} \Rightarrow $poisson$(\mu$,$k)

Hypergeometric Distribution: P(X=k) = \frac{\binom{M}{k} \cdot \binom{N-M}{n-k}}{\binom{N}{n}} \Rightarrow $hypergeomdist$(k$,$M$,$N$,$n)

Normal Distribution: \Phi_{\mu,\sigma}(x) = \Phi \left( \frac{x-\mu}{\sigma} \right) \Rightarrow $normdist$(x,\mu,\sigma,$true/false$)

\Rightarrow $norminv$(P(X),0,1)

Standard Deviation: \sigma := \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_i - \bar{x})^2} \Rightarrow $stdev$(x_1,x_2,\hdots,x_n)

Experimental Standard Deviation: \sigma := \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i - \bar{x})^2} \Rightarrow $stdevp$(x_1,x_2,\hdots,x_n)

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V1ru8 on January 31st 2008 in Math

Helpfully functions in mathematica for cryptographic

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V1ru8 on January 4th 2008 in Math