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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

( n r ) = n ! ( n r ) ! r !

Formula 3: binomial distribution

X ~ B ( n , p )

P ( X = x ) = ( n x ) 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 ) = ( ( r x ) ( b n x ) ( r + b n ) )

Formula 6: poisson distribution

X ~ P ( μ )

P ( X = x ) = μ x e μ x !

Formula 7: uniform distribution

X ~ U ( a , b )

f ( X ) = 1 b a , a < x < b

Formula 8: exponential distribution

X ~ E x p ( m )

f ( x ) = m e m x m > 0 , x 0

Formula 9: normal distribution

X ~ N ( μ , σ 2 )

f ( x ) = 1 σ 2 π e ( x μ ) 2 2 σ 2 , < x <

Formula 10: gamma function

Γ ( z ) = 0 x z 1 e x d x z > 0

Γ ( 1 2 ) = 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 ) = ( 1 + x 2 n ) ( n + 1 ) 2 Γ ( n + 1 2 ) Γ ( n 2 )

X = Z 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 ) = x n 2 2 e x 2 2 n 2 Γ ( 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 ) = Γ ( u + v 2 ) Γ ( u 2 ) Γ ( v 2 ) ( u v ) u 2 x ( u 2 1 ) [ 1 + ( u v ) x 0.5 ( u + v ) ]

X = 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           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 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 greater than or equal to same
Discrete Random Variables 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 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 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 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 α 2 student t with a /2 area in right tail same
Confidence Intervals p ; p ^ p -prime; p -hat sample proportion of success
Confidence Intervals q ; 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 X 1 ¯ 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 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

3xy^2√[x^3y^2/(12(x^3y)^2)]
Esther Reply
what is probability
Esther
what is probability
Esther
what is probability
Esther
Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
Dewan
mean 0 and standard deviation 1 .using area table find P(X>3)
Naeem Reply
what is terms data?
Mohsin Reply
define the types of data?
Mohsin
define the number of classes?
Mohsin
define the class limt?
Mohsin
define the class frequency and class interval ?
Mohsin
define class boundaries
George
Your home address nominal Interval ratio ordinal
MD
home address is nominal
Awel
what is axioms of probability
Khaleed Reply
characteristics of statistic
Safi Reply
a measure of cntral tendency is a quantitative value that tends to locate in some sense the middle of a set of data
khan Reply
in a large metropolitan area
Vernon Reply
a lecturer claims that his students score an average of 55 marks in their statistics test. the object supervisor wants to know wether the lecturer's claims is acceptable or not.what is the posible tail of the test?
Karen
2
J-zil
the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah Reply
what the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah
option please
Dewan
systematic
Dewan
any one send me the notes of these chpt if possible introduction to statistics measure of centeral tendency or average measure of dispensation moments and skewness presentation of data
Aqsa Reply
Kindly send me these notes.
Naheed
what is a regression, and what is it primarily used for
Denisha Reply
assume the sample populations do not have equal standard deviations and use the 0.05 significance level
Nokuthula Reply
what is the solution to this question?
Manbyen Reply
hi
Dewan
hello
Learn
hi please tell
Dewan
The controls that are usually used are
Rushikesh Reply
what is math
Rushikesh
the controls that are usually used in quality controls and also controls a process is key tool used in run chat, control chat and design of experiment etc.,
Sravanthi
mean is number that occurs frequently in a giving data
Chinedu Reply
That places the mode and the mean as the same thing. I'd define the mean as the ratio of the total sum of variables to the variable count, and it assigns the variables a similar value across the board.
Samsicker
what is mean
John Reply

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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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