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When the English says: | Interpret this as: |
---|---|
X is at least 4. | X ≥ 4 |
The minimum of X is 4. | X ≥ 4 |
X is no less than 4. | X ≥ 4 |
X is greater than or equal to 4. | X ≥ 4 |
X is at most 4. | X ≤ 4 |
The maximum of X is 4. | X ≤ 4 |
X is no more than 4. | X ≤ 4 |
X is less than or equal to 4. | X ≤ 4 |
X does not exceed 4. | X ≤ 4 |
X is greater than 4. | X >4 |
X is more than 4. | X >4 |
X exceeds 4. | X >4 |
X is less than 4. | X <4 |
There are fewer X than 4. | X <4 |
X is 4. | X = 4 |
X is equal to 4. | X = 4 |
X is the same as 4. | X = 4 |
X is not 4. | X ≠ 4 |
X is not equal to 4. | X ≠ 4 |
X is not the same as 4. | X ≠ 4 |
X is different than 4. | X ≠ 4 |
$0!=1\text{}$
$P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right){p}^{x}{q}^{n-x}$ , for
$x=0,1,2,...,n$
$P(X=x)={q}^{x-1}p$ , for
$x=1,2,3,...$
$P\text{(}X=x\text{)}=\left(\frac{\left(\genfrac{}{}{0ex}{}{r}{x}\right)\left(\genfrac{}{}{0ex}{}{b}{n-x}\right)}{\left(\genfrac{}{}{0ex}{}{r+b}{n}\right)}\right)$
$P\text{(}X=x\text{)}=\frac{{\mu}^{x}{e}^{-\mu}}{x!}$
$f(X)=\frac{1}{b-a}$ ,
$a<x<b$
$f(x)=m{e}^{-mx}m>0,x\ge 0$
$f\text{(}x\text{)}=\frac{1}{\sigma \sqrt{2\pi}}{e}^{\frac{{-(x-\mu )}^{2}}{{2\sigma}^{2}}}$ ,
$\phantom{\rule{12pt}{0ex}}\u2013\infty <x<\infty $
$\Gamma \left(\frac{1}{2}\right)=\sqrt{\pi}$
$\Gamma (m+1)=m!$ for $m$ , a nonnegative integer
otherwise:
$\Gamma (a+1)=a\Gamma (a)$
$f\text{(}x\text{)}=\frac{{\left(1+\frac{{x}^{2}}{n}\right)}^{\frac{-(n+1)}{2}}\Gamma \left(\frac{n+1}{2}\right)}{\sqrt{\mathrm{n\pi}}\Gamma \left(\frac{n}{2}\right)}$
$X=\frac{Z}{\sqrt{\frac{Y}{n}}}$
$Z\phantom{\rule{2px}{0ex}}~\phantom{\rule{2px}{0ex}}N(0,1),\phantom{\rule{2px}{0ex}}Y\phantom{\rule{2px}{0ex}}~\phantom{\rule{2px}{0ex}}{{\rm X}}_{df}^{2}$ ,
$n$ = degrees of freedom
$f\text{(}x\text{)}=\frac{{x}^{\frac{n-2}{2}}{e}^{\frac{-x}{2}}}{{2}^{\frac{n}{2}}\Gamma \left(\frac{n}{2}\right)}$ ,
$x>0$ ,
$n$ = positive integer and degrees of freedom
$df(n)\phantom{\rule{2px}{0ex}}=\phantom{\rule{2px}{0ex}}$ degrees of freedom for the numerator
$df(d)\phantom{\rule{2px}{0ex}}=\phantom{\rule{2px}{0ex}}$ degrees of freedom for the denominator
$f(x)=\frac{\Gamma (\frac{u+v}{2})}{\Gamma (\frac{u}{2})\Gamma (\frac{v}{2})}{(\frac{u}{v})}^{\frac{u}{2}}{x}^{(\frac{u}{2}-1)}[1+(\frac{u}{v}){x}^{-0.5(u+v)}]$
$X=\frac{{Y}_{u}}{{W}_{v}}$ , $Y$ , $W$ are chi-square
Chapter (1st used) | Symbol | Spoken | Meaning |
---|---|---|---|
Sampling and Data | $\sqrt{\begin{array}{c}\text{}\\ \text{}\end{array}}$ | The square root of | same |
Sampling and Data | $\pi $ | Pi | 3.14159… (a specific number) |
Descriptive Statistics | Q _{1} | Quartile one | the first quartile |
Descriptive Statistics | Q _{2} | Quartile two | the second quartile |
Descriptive Statistics | Q _{3} | Quartile three | the third quartile |
Descriptive Statistics | IQR | interquartile range | Q _{3} – Q _{1} = IQR |
Descriptive Statistics | $\overline{x}$ | x-bar | sample mean |
Descriptive Statistics | $\mu $ | mu | population mean |
Descriptive Statistics | s s _{x} sx | s | sample standard deviation |
Descriptive Statistics | ${s}^{2}$ ${s}_{x}^{2}$ | s squared | sample variance |
Descriptive Statistics | $\sigma $ ${\sigma}_{x}$ σx | sigma | population standard deviation |
Descriptive Statistics | ${\sigma}^{2}$ ${\sigma}_{x}^{2}$ | sigma squared | population variance |
Descriptive Statistics | $\Sigma $ | capital sigma | sum |
Probability Topics | $\left\{\right\}$ | brackets | set notation |
Probability Topics | $S$ | S | sample space |
Probability Topics | $A$ | Event A | event A |
Probability Topics | $P\left(A\right)$ | probability of A | probability of A occurring |
Probability Topics | $P(\mathit{\text{A}}\text{|}\mathit{\text{B}})$ | probability of A given B | prob. of A occurring given B has occurred |
Probability Topics | $P(A\text{OR}B)$ | prob. of A or B | prob. of A or B or both occurring |
Probability Topics | $P(A\text{AND}B)$ | prob. of A and B | prob. of both A and B occurring (same time) |
Probability Topics | A ′ | A-prime, complement of A | complement of A, not A |
Probability Topics | P ( A ') | prob. of complement of A | same |
Probability Topics | G _{1} | green on first pick | same |
Probability Topics | P ( G _{1} ) | prob. of green on first pick | same |
Discrete Random Variables | prob. distribution function | same | |
Discrete Random Variables | X | X | the random variable X |
Discrete Random Variables | X ~ | the distribution of X | same |
Discrete Random Variables | B | binomial distribution | same |
Discrete Random Variables | G | geometric distribution | same |
Discrete Random Variables | H | hypergeometric dist. | same |
Discrete Random Variables | P | Poisson dist. | same |
Discrete Random Variables | $\lambda $ | Lambda | average of Poisson distribution |
Discrete Random Variables | $\ge $ | greater than or equal to | same |
Discrete Random Variables | $\le $ | less than or equal to | same |
Discrete Random Variables | = | equal to | same |
Discrete Random Variables | ≠ | not equal to | same |
Continuous Random Variables | f ( x ) | f of x | function of x |
Continuous Random Variables | prob. density function | same | |
Continuous Random Variables | U | uniform distribution | same |
Continuous Random Variables | Exp | exponential distribution | same |
Continuous Random Variables | k | k | critical value |
Continuous Random Variables | f ( x ) = | f of x equals | same |
Continuous Random Variables | m | m | decay rate (for exp. dist.) |
The Normal Distribution | N | normal distribution | same |
The Normal Distribution | z | z -score | same |
The Normal Distribution | Z | standard normal dist. | same |
The Central Limit Theorem | CLT | Central Limit Theorem | same |
The Central Limit Theorem | $\overline{X}$ | X -bar | the random variable X -bar |
The Central Limit Theorem | ${\mu}_{x}$ | mean of X | the average of X |
The Central Limit Theorem | ${\mu}_{\overline{x}}$ | mean of X -bar | the average of X -bar |
The Central Limit Theorem | ${\sigma}_{x}$ | standard deviation of X | same |
The Central Limit Theorem | ${\sigma}_{\overline{x}}$ | standard deviation of X -bar | same |
The Central Limit Theorem | $\Sigma X$ | sum of X | same |
The Central Limit Theorem | $\Sigma x$ | sum of x | same |
Confidence Intervals | CL | confidence level | same |
Confidence Intervals | CI | confidence interval | same |
Confidence Intervals | EBM | error bound for a mean | same |
Confidence Intervals | EBP | error bound for a proportion | same |
Confidence Intervals | t | Student's t -distribution | same |
Confidence Intervals | df | degrees of freedom | same |
Confidence Intervals | ${t}_{\frac{\alpha}{2}}$ | student t with a /2 area in right tail | same |
Confidence Intervals | $p\prime $ ; $\hat{p}$ | p -prime; p -hat | sample proportion of success |
Confidence Intervals | $q\prime $ ; $\hat{q}$ | q -prime; q -hat | sample proportion of failure |
Hypothesis Testing | ${H}_{0}$ | H -naught, H -sub 0 | null hypothesis |
Hypothesis Testing | ${H}_{a}$ | H-a , H -sub a | alternate hypothesis |
Hypothesis Testing | ${H}_{1}$ | H -1, H -sub 1 | alternate hypothesis |
Hypothesis Testing | $\alpha $ | alpha | probability of Type I error |
Hypothesis Testing | $\beta $ | beta | probability of Type II error |
Hypothesis Testing | $\overline{X1}-\overline{X2}$ | X 1-bar minus X 2-bar | difference in sample means |
Hypothesis Testing | ${\mu}_{1}-{\mu}_{2}$ | mu -1 minus mu -2 | difference in population means |
Hypothesis Testing | ${{P}^{\prime}}_{1}-{{P}^{\prime}}_{2}$ | P 1-prime minus P 2-prime | difference in sample proportions |
Hypothesis Testing | ${p}_{1}-{p}_{2}$ | p 1 minus p 2 | difference in population proportions |
Chi-Square Distribution | ${{\rm X}}^{2}$ | Ky -square | Chi-square |
Chi-Square Distribution | $O$ | Observed | Observed frequency |
Chi-Square Distribution | $E$ | Expected | Expected frequency |
Linear Regression and Correlation | y = a + bx | y equals a plus b-x | equation of a line |
Linear Regression and Correlation | $\hat{y}$ | y -hat | estimated value of y |
Linear Regression and Correlation | $r$ | correlation coefficient | same |
Linear Regression and Correlation | $\epsilon $ | error | same |
Linear Regression and Correlation | SSE | Sum of Squared Errors | same |
Linear Regression and Correlation | 1.9 s | 1.9 times s | cut-off value for outliers |
F -Distribution and ANOVA | F | F -ratio | F -ratio |
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