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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

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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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