0.6 Mathematical phrases, symbols, and formulas

Introductory statistics Page 1 / 1

English phrases written mathematically

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

Formulas

Formula 1: factorial

n! = n (n - 1) (n - 2) . . . (1)

$0! = 1$

Formula 2: combinations

(\begin{array}{l} n \\ r \end{array}) = \frac{n!}{(n - r)! r!}

Formula 3: binomial distribution

X ~ B (n, p)

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x}$ , for $x = 0, 1, 2, . . ., n$

Formula 4: geometric distribution

X ~ G (p)

$P (X = x) = q^{x - 1} p$ , for $x = 1, 2, 3, . . .$

Formula 5: hypergeometric distribution

X ~ H (r, b, n)

$P (X = x) = (\frac{(\binom{r}{x}) (\binom{b}{n - x})}{(\binom{r + b}{n})})$

Formula 6: poisson distribution

X ~ P (μ)

$P (X = x) = \frac{μ^{x} e^{- μ}}{x!}$

Formula 7: uniform distribution

X ~ U (a, b)

$f (X) = \frac{1}{b - a}$ , $a < x < b$

Formula 8: exponential distribution

X ~ E x p (m)

$f (x) = m e^{- m x} m > 0, x \geq 0$

Formula 9: normal distribution

X ~ N (μ, σ^{2})

$f (x) = \frac{1}{σ \sqrt{2 π}} e^{\frac{{- (x - μ)}^{2}}{{2 σ}^{2}}}$ , $- \infty < x < \infty$

Formula 10: gamma function

Γ (z) = {\int^{​}}_{\infty}^{0} x^{z - 1} e^{- x} d x

z > 0

$Γ (\frac{1}{2}) = \sqrt{π}$

$Γ (m + 1) = m!$ for $m$ , a nonnegative integer

otherwise: $Γ (a + 1) = a Γ (a)$

Formula 11: student's t -distribution

X ~ t_{d f}

$f (x) = \frac{{(1 + \frac{x^{2}}{n})}^{\frac{- (n + 1)}{2}} Γ (\frac{n + 1}{2})}{\sqrt{nπ} Γ (\frac{n}{2})}$

$X = \frac{Z}{\sqrt{\frac{Y}{n}}}$

$Z ~ N (0, 1), Y ~ Χ_{d f}^{2}$ , $n$ = degrees of freedom

Formula 12: chi-square distribution

X ~ Χ_{d f}^{2}

$f (x) = \frac{x^{\frac{n - 2}{2}} e^{\frac{- x}{2}}}{2^{\frac{n}{2}} Γ (\frac{n}{2})}$ , $x > 0$ , $n$ = positive integer and degrees of freedom

Formula 13: f distribution

X ~ F_{d f (n), d f (d)}

$d f (n) =$ degrees of freedom for the numerator

$d f (d) =$ degrees of freedom for the denominator

$f (x) = \frac{Γ (\frac{u + v}{2})}{Γ (\frac{u}{2}) Γ (\frac{v}{2})} {(\frac{u}{v})}^{\frac{u}{2}} x^{(\frac{u}{2} - 1)} [1 + (\frac{u}{v}) x^{- 0.5 (u + v)}]$

$X = \frac{Y_{u}}{W_{v}}$ , $Y$ , $W$ are chi-square

Symbols and their meanings

Symbols and their meanings
Chapter (1st used)	Symbol	Spoken	Meaning
Sampling and Data	$\sqrt{\begin{matrix} \end{matrix}}$	The square root of	same
Sampling and Data	$π$	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	$\bar{x}$	x-bar	sample mean
Descriptive Statistics	$μ$	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	$σ$ $σ_{x}$ σx	sigma	population standard deviation
Descriptive Statistics	$σ^{2}$ $σ_{x}^{2}$	sigma squared	population variance
Descriptive Statistics	$Σ$	capital sigma	sum
Probability Topics	${}$	brackets	set notation
Probability Topics	$S$	S	sample space
Probability Topics	$A$	Event A	event A
Probability Topics	$P (A)$	probability of A	probability of A occurring
Probability Topics	$P (A \| B)$	probability of A given B	prob. of A occurring given B has occurred
Probability Topics	$P (A OR B)$	prob. of A or B	prob. of A or B or both occurring
Probability Topics	$P (A AND B)$	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	PDF	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	$λ$	Lambda	average of Poisson distribution
Discrete Random Variables	$\geq$	greater than or equal to	same
Discrete Random Variables	$\leq$	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	pdf	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	$\bar{X}$	X -bar	the random variable X -bar
The Central Limit Theorem	$μ_{x}$	mean of X	the average of X
The Central Limit Theorem	$μ_{\bar{x}}$	mean of X -bar	the average of X -bar
The Central Limit Theorem	$σ_{x}$	standard deviation of X	same
The Central Limit Theorem	$σ_{\bar{x}}$	standard deviation of X -bar	same
The Central Limit Theorem	$Σ X$	sum of X	same
The Central Limit Theorem	$Σ x$	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	$t_{\frac{α}{2}}$	student t with a /2 area in right tail	same
Confidence Intervals	$p'$ ; $\hat{p}$	p -prime; p -hat	sample proportion of success
Confidence Intervals	$q'$ ; $\hat{q}$	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	$α$	alpha	probability of Type I error
Hypothesis Testing	$β$	beta	probability of Type II error
Hypothesis Testing	$\bar{X 1} - \bar{X 2}$	X 1-bar minus X 2-bar	difference in sample means
Hypothesis Testing	$μ_{1} - μ_{2}$	mu -1 minus mu -2	difference in population means
Hypothesis Testing	${P^{'}}_{1} - {P^{'}}_{2}$	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	$Χ^{2}$	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	$ε$	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

Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.

Widad Reply

can you send the book attached ?

Ariel

What is economics

Widad Reply

the study of how humans make choices under conditions of scarcity

AI-Robot

U(x,y) = (x×y)1/2 find mu of x for y

Desalegn Reply

U(x,y) = (xÃy)1/2 find mu of x for y

Desalegn

what is ecnomics

Jan Reply

this is the study of how the society manages it's scarce resources

Belonwu

what is macroeconomic

John Reply

macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.

husaini

etc

husaini

difference between firm and industry

husaini Reply

what's the difference between a firm and an industry

Abdul

firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅

Abdulraufu

Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?

Toofiq Reply

explain standard reason why economic is a science

innocent Reply

factors influencing supply

Petrus Reply

what is economic.

Milan Reply

scares means__________________ends resources. unlimited

Jan

economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses

Jan

calculate the profit maximizing for demand and supply

Zarshad Reply

Why qualify 28 supplies

Milan

what are explicit costs

Nomsa Reply

out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials

AI-Robot

concepts of supply in microeconomics

David Reply

economic overview notes

Amahle Reply

identify a demand and a supply curve

Salome Reply

i don't know

Parul

there's a difference

Aryan

Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods

Israr

Hi Sir please how do u calculate Cross elastic demand and income elastic demand?

Abari

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Source: OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18

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