Appendix f mathematical phrases, symbols, and formulas

Chapter 1st used Symbol Spoken MeaningDescriptive 2 σx2 sigma squared population variance Descriptive Probability Topics PA probability of A probability of A occurring Probability Topics

Appendix F: Mathematical

Phrases, Symbols, and

Formulas

By:

OpenStaxCollege

English Phrases Written Mathematically

When the English says: Interpret this as:

The minimum of X is 4 X ≥ 4

X is greater than or equal to 4 X ≥ 4

The maximum of X is 4 X ≤ 4

X is less than or equal to 4 X ≤ 4

There are fewer X than 4 X < 4

When the English says: Interpret this as:

Formulas

Formula 1: Factorial n! = n(n − 1)(n − 2) (1)

0! = 1

Formula 2: Combinations( n

r ) = (n − r)! r ! n !

Formula 3: Binomial DistributionX ~ B(n, p)

P(X = x) =( n

x )p x q n − x , for x = 0, 1, 2, , n Formula 4: Geometric DistributionX ~ G(p)

P(X = x) = q x − 1 p, for x = 1, 2, 3,

Formula 5: Hypergeometric DistributionX ~ H(r, b, n)

P(X = x) =( (r

x)( b

n − x) (r + b

n ) )

Formula 6: Poisson DistributionX ~ P(μ)

P(X = x) = μx e x !− μ

Formula 7: Uniform DistributionX ~ U(a, b)

f(X) = b − a1 , a < x < b

Formula 8: Exponential DistributionX ~ Exp(m)

f(x) = me − mx m > 0, x ≥ 0

Formula 9: Normal DistributionX ~ N(μ, σ2)

f(x) = σ√12πe

− (x − μ)2

2σ2 , – ∞ < x < ∞

Formula 10: Gamma FunctionΓ(z) =

0

∫

∞

x z − 1 e − x dx z > 0

Γ(1

2) =√π

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

otherwise: Γ(a + 1) = aΓ(a)

Formula 11: Student's t-distributionX ~ t df

f(x) = (1 +x2 n)−(n + 12 )Γ(n + 1

2 )

√ nπΓ(n

2)

X = Z

√Y

n

Z ~ N(0, 1 ), Y ~ Χ df2, n = degrees of freedom

Formula 12: Chi-Square DistributionX ~ Χ df2

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 DistributionX ~ F df(n), df(d)

df(d) = degrees of freedom for the denominator

f(x) = Γ(

u + v

2 )

Γ(u2)Γ(2v)(u v)u2x(u2 − 1)[1 + (u v )x − 0.5(u + v)]

X = W Y u

v , Y, W are chi-square

Symbols and Their Meanings

Symbols and their Meanings

Sampling and Data √ The square root of same

number) Descriptive

Descriptive

Descriptive

Statistics Q3 Quartile three the third quartile

Descriptive

Statistics IQR interquartile range Q3– Q1= IQR

Descriptive

Descriptive

Descriptive

Descriptive

2

Descriptive

population standard deviation

Chapter (1st used) Symbol Spoken Meaning

Descriptive

2

σx2 sigma squared population variance

Descriptive

Probability Topics P(A) probability of A probability of A occurring Probability Topics P(A|B) probability of Agiven B prob of A occurring givenB 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 Boccurring (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 G1 green on first pick same

Probability Topics P(G1) prob of green on

Discrete Random

prob distribution

Discrete Random

Discrete Random

Discrete Random

binomial distribution same

Chapter (1st used) Symbol Spoken Meaning

Discrete Random

hypergeometric

Discrete Random

Discrete Random

average of Poisson distribution

Discrete Random

greater than or

Discrete Random

Discrete Random

Discrete Random

Continuous Random

Continuous Random

prob density

Continuous Random

Continuous Random

exponential distribution same Continuous Random

Continuous Random

Continuous Random

The Normal

The Normal

Chapter (1st used) Symbol Spoken Meaning

The Normal

standard normal

The Central Limit

Central Limit

The Central Limit

The Central Limit

The Central Limit

The Central Limit

standard deviation

The Central Limit

standard deviation

The Central Limit

The Central Limit

Confidence

Confidence

Confidence

error bound for a

Confidence

error bound for a

Confidence

Student's

t-distribution same Confidence

Chapter (1st used) Symbol Spoken Meaning

Confidence

^

p p-prime; p-hat sample proportion ofsuccess

Confidence

^

q q-prime; q-hat sample proportion offailure

Hypothesis Testing H0 H-naught, H-sub 0 null hypothesis

Hypothesis Testing H a H-a, H-sub a alternate hypothesis

Hypothesis Testing H1 H-1, H-sub 1 alternate hypothesis

Hypothesis Testing α alpha probability of Type I error

Hypothesis Testing β beta probability of Type IIerror

Hypothesis Testing ¯X1 −¯X2 X1-bar minus

X2-bar

difference in sample means

Hypothesis Testing μ1 − μ2 mu-1 minus mu-2 difference in population

means

Hypothesis Testing P′1− P′2 P1-prime minus

P2-prime

difference in sample proportions

Hypothesis Testing p1− p2 p1 minus p2 difference in population

proportions Chi-Square

Chi-Square

Chi-Square

Linear Regression

and Correlation y = a + bx y equals a plus b-x equation of a line

Linear Regression

and Correlation

^

Linear Regression

and Correlation r

correlation

Chapter (1st used) Symbol Spoken Meaning

Linear Regression

Linear Regression

and Correlation SSE

Sum of Squared

Linear Regression

and Correlation 1.9s 1.9 times s cut-off value for outliers

F-Distribution and