V1ru8

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)$