# Selected Formulas

# Chapter 2

$\text{RelativeFrequency}=\left(\text{frequency}\right)/n$

$\overline{x}={\displaystyle \frac{\Sigma x}{n}}$

${s}^{2}={\displaystyle \frac{\Sigma {\left(x-\overline{x}\right)}^{2}}{n-1}}={\displaystyle \frac{\Sigma {x}^{2}-{\displaystyle \frac{{\left(\Sigma x\right)}^{2}}{n}}}{n-1}}$

$s=\sqrt{{s}^{2}}$

$z={\displaystyle \frac{x-\mu}{\sigma}}={\displaystyle \frac{x-\overline{x}}{s}}$

$\text{Chebyshev}=\text{Atleast}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(1-{\displaystyle \frac{1}{{k}^{2}}}\right)100\%$

$\text{IQR}\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}{Q}_{\text{U}}-{Q}_{\text{L}}$

# Chapter 3

$P\left({A}^{c}\right)=1-P\left(A\right)$

$\begin{array}{rrr}\hfill P\left(A\cup B\right)& \hfill =& P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\hfill \\ \hfill & \hfill =& P\left(A\right)+P\left(B\right)\text{\hspace{0.17em}}\text{if}A\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}B\text{\hspace{0.17em}}\text{mutually}\text{\hspace{0.17em}}\text{exclusive}\hfill \end{array}$

$\begin{array}{rrr}\hfill P\left(A\cap B\right)& \hfill =& P\left(A|B\right)\cdot P\left(B\right)=P\left(B|A\right)\cdot P\left(A\right)\hfill \\ \hfill & \hfill =& P\left(A\right)\cdot P\left(B\right)\text{\hspace{0.17em}}\text{if}A\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}B\text{\hspace{0.17em}}\text{independent}\hfill \end{array}$

$P\left(A|B\right)={\displaystyle \frac{P\left(A\cap B\right)}{P\left(B\right)}}$

$\left(\begin{array}{c}N\\ n\end{array}\right)={\displaystyle \frac{N!}{n!\left(N-n\right)!}}$

# Chapter 4

Random Variable | Prob. Dist’n | Mean | Variance |
---|---|---|---|

General Discrete: |
Table, formula, or graph for ... |

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