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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

answer for question 3
Awuah Reply
what are the terminologies in statistics?
Abranti Reply
population sample statistic parameter etc..
AF
the mode of the table class 3_7 8_12 13 _17 frequency 10 25 19
Samah Reply
25
AF
how touching
Ahmad
what..?
AF
how am I here
Angelo
how?
Najeeb
what?
Najeeb
i didn't know this app had a chat
Angelo
9.8
Rasika
I think 25 is higher frequency
AF
compare to 10 and 19
AF
by using formula...?
AF
L+((f1-f0)÷2f1-f0-f2)×h by this formula using ans is 9.8
Rasika
Me too I think the highest frequency is 25
Sebili
how is useful
how is stem and leaf plot or display differ from double stem and leaf plot or display
Sebili Reply
What is the variances of 568
Helen Reply
what u asking...
friend
what variance would have a single value..?
friend
variance happened only in a group of values..
friend
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
friend
compare the relative adrantages and disadvantages of mean mediam and made
News
What is the variances of 258
Helen Reply
66,564
Mampy
what is the sample size if the degree of freedom is 25?
Arthur Reply
26..
friend
25
Tariku
27
Tariku
degrees of freedom may differ with respect to distribution...so tell which distribution you have selected...?
friend
my distribution is 27
Tariku
what is degree of freedom?
Rohit
how to understand statistics
Edwin Reply
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
Yamin Reply
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija 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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