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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

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Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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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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