{"id":890,"date":"2017-10-19T22:17:19","date_gmt":"2017-10-19T22:17:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=back-matter&p=890"},"modified":"2017-10-19T22:17:19","modified_gmt":"2017-10-19T22:17:19","slug":"appendix-f-mathematical-phrases-symbols-and-formulas","status":"publish","type":"back-matter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/back-matter\/appendix-f-mathematical-phrases-symbols-and-formulas\/","title":{"raw":"Appendix F: Mathematical Phrases, Symbols, and Formulas","rendered":"Appendix F: Mathematical Phrases, Symbols, and Formulas"},"content":{"raw":"

English Phrases Written Mathematically<\/h1>\n
When the English says:<\/th>\nInterpret this as:<\/th>\n<\/tr><\/thead>
X<\/em> is at least 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>
The minimum of X<\/em> is 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>
X<\/em> is no less than 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>
X<\/em> is greater than or equal to 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>
X<\/em> is at most 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>
The maximum of X<\/em> is 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>
X<\/em> is no more than 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>
X<\/em> is less than or equal to 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>
X<\/em> does not exceed 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>
X<\/em> is greater than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>
X<\/em> is more than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>
X<\/em> exceeds 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>
X<\/em> is less than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>
There are fewer X<\/em> than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>
X<\/em> is 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>
X<\/em> is equal to 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>
X<\/em> is the same as 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>
X<\/em> is not 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>
X<\/em> is not equal to 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>
X<\/em> is not the same as 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>
X<\/em> is different than 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr><\/tbody><\/table><\/section>

Formulas<\/h1>\n

Formula 1: Factorial<\/span>n<\/span>!<\/span>=<\/span>n<\/span>(<\/span>n<\/span>\u2212<\/span>1<\/span>)<\/span>(<\/span>n<\/span>\u2212<\/span>2<\/span>)<\/span>.<\/span>.<\/span>.<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

0<\/span>!<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 2: Combinations<\/span>(<\/span>n<\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span>n<\/span>!<\/span><\/span>(<\/span>n<\/span>\u2212<\/span>r<\/span>)<\/span>!<\/span>r<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 3: Binomial Distribution<\/span>X<\/span>~<\/span>B<\/span>(<\/span>n<\/span>,<\/span>p<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>(<\/span>n<\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>p<\/span>x<\/span><\/span>q<\/span>n<\/span>\u2212<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, for x<\/span>=<\/span>0<\/span>,<\/span>1<\/span>,<\/span>2<\/span>,<\/span>.<\/span>.<\/span>.<\/span>,<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 4: Geometric Distribution<\/span>X<\/span>~<\/span>G<\/span>(<\/span>p<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>q<\/span>x<\/span>\u2212<\/span>1<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, for x<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>.<\/span>.<\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 5: Hypergeometric Distribution<\/span>X<\/span>~<\/span>H<\/span>(<\/span>r<\/span>,<\/span>b<\/span>,<\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>(<\/span>(<\/span>r<\/span>x<\/span><\/span>)<\/span><\/span>(<\/span>b<\/span>n<\/span>\u2212<\/span>x<\/span><\/span><\/span>)<\/span><\/span><\/span>(<\/span>r<\/span>+<\/span>b<\/span><\/span>n<\/span><\/span>)<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 6: Poisson Distribution<\/span>X<\/span>~<\/span>P<\/span>(<\/span>\u03bc<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>\u03bc<\/span>x<\/span><\/span>e<\/span>\u2212<\/span>\u03bc<\/span><\/span><\/span><\/span>x<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 7: Uniform Distribution<\/span>X<\/span>~<\/span>U<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>X<\/span>)<\/span>=<\/span>1<\/span>b<\/span>\u2212<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, a<\/span><<\/span>x<\/span><<\/span>b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 8: Exponential Distribution<\/span>X<\/span>~<\/span>E<\/span>x<\/span>p<\/span>(<\/span>m<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>m<\/span>e<\/span>\u2212<\/span>m<\/span>x<\/span><\/span><\/span>m<\/span>><\/span>0<\/span>,<\/span>x<\/span>\u2265<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 9: Normal Distribution<\/span>X<\/span>~<\/span>N<\/span>(<\/span>\u03bc<\/span>,<\/span>\u03c3<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>1<\/span>\u03c3<\/span>2<\/span>\u03c0<\/span><\/span>\u221a<\/span><\/span><\/span>e<\/span>\u2212<\/span>(<\/span>x<\/span>\u2212<\/span>\u03bc<\/span>)<\/span><\/span>2<\/span><\/span>2<\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> , \u2013<\/span>\u221e<\/span><<\/span>x<\/span><<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 10: Gamma Function<\/span>\u0393<\/span>(<\/span>z<\/span>)<\/span>=<\/span>\u222b<\/span><\/span><\/span><\/span><\/span>\u221e<\/span>0<\/span><\/span>x<\/span>z<\/span>\u2212<\/span>1<\/span><\/span><\/span>e<\/span>\u2212<\/span>x<\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span> z<\/span>><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0393<\/span>(<\/span>1<\/span>2<\/span><\/span>)<\/span>=<\/span>\u03c0<\/span><\/span>\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0393<\/span>(<\/span>m<\/span>+<\/span>1<\/span>)<\/span>=<\/span>m<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span> for m<\/span><\/span><\/span><\/span><\/span><\/span>, a nonnegative integer<\/p>\n

otherwise: \u0393<\/span>(<\/span>a<\/span>+<\/span>1<\/span>)<\/span>=<\/span>a<\/span>\u0393<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

\n\n<\/div>\n

Formula 11: Student's t<\/em>-distribution<\/span>X<\/span>~<\/span>t<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>(<\/span>1<\/span>+<\/span>x<\/span>2<\/span><\/span>n<\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span>(<\/span>n<\/span>+<\/span>1<\/span>)<\/span><\/span>2<\/span><\/span><\/span>\u0393<\/span>(<\/span>n<\/span>+<\/span>1<\/span><\/span>2<\/span><\/span>)<\/span><\/span><\/span>n\u03c0<\/span><\/span>\u221a<\/span>\u0393<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

X<\/span>=<\/span>Z<\/span>Y<\/span>n<\/span><\/span><\/span>\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Z<\/span>~<\/span>N<\/span>(<\/span>0<\/span>,<\/span>1<\/span>),<\/span>Y<\/span>~<\/span>\u03a7<\/span>2<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, n<\/span><\/span><\/span><\/span><\/span><\/span> = degrees of freedom<\/p>\n\n

\n\n<\/div>\n

Formula 12: Chi-Square Distribution<\/span>X<\/span>~<\/span>\u03a7<\/span>2<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>x<\/span>n<\/span>\u2212<\/span>2<\/span><\/span>2<\/span><\/span><\/span>e<\/span>\u2212<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>2<\/span>n<\/span>2<\/span><\/span><\/span>\u0393<\/span>(<\/span>n<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, x<\/span>><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span> , n<\/span><\/span><\/span><\/span><\/span><\/span> = positive integer and degrees of freedom<\/p>\n\n

\n\n<\/div>\n

Formula 13: F Distribution<\/span>X<\/span>~<\/span>F<\/span>d<\/span>f<\/span>(<\/span>n<\/span>)<\/span>,<\/span>d<\/span>f<\/span>(<\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

d<\/span>f<\/span>(<\/span>n<\/span>)<\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>degrees of freedom for the numerator<\/p>\n

d<\/span>f<\/span>(<\/span>d<\/span>)<\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>degrees of freedom for the denominator<\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>\u0393<\/span>(<\/span>u<\/span>+<\/span>v<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\u0393<\/span>(<\/span>u<\/span>2<\/span><\/span>)<\/span>\u0393<\/span>(<\/span>v<\/span>2<\/span><\/span>)<\/span><\/span><\/span>(<\/span>u<\/span>v<\/span><\/span>)<\/span><\/span>u<\/span>2<\/span><\/span><\/span><\/span>x<\/span>(<\/span>u<\/span>2<\/span><\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span>[<\/span>1<\/span>+<\/span>(<\/span>u<\/span>v<\/span><\/span>)<\/span>x<\/span>\u2212<\/span>0.5<\/span>(<\/span>u<\/span>+<\/span>v<\/span>)<\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

X<\/span>=<\/span>Y<\/span>u<\/span><\/span>W<\/span>v<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, Y<\/span><\/span><\/span><\/span><\/span><\/span>, W<\/span><\/span><\/span><\/span><\/span><\/span> are chi-square<\/p>\n\n<\/section>

Symbols and Their Meanings<\/h1>\n
Symbols and their Meanings<\/span><\/caption>\n
Chapter (1st used)<\/th>\nSymbol<\/th>\nSpoken<\/th>\nMeaning<\/th>\n<\/tr><\/thead>
Sampling and Data<\/td>\n\u00a0\u00a0<\/span><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nThe square root of<\/td>\nsame<\/td>\n<\/tr>
Sampling and Data<\/td>\n\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nPi<\/td>\n3.14159\u2026 (a specific number)<\/td>\n<\/tr>
Descriptive Statistics<\/td>\nQ<\/em>1<\/sub><\/td>\nQuartile one<\/td>\nthe first quartile<\/td>\n<\/tr>
Descriptive Statistics<\/td>\nQ<\/em>2<\/sub><\/td>\nQuartile two<\/td>\nthe second quartile<\/td>\n<\/tr>
Descriptive Statistics<\/td>\nQ<\/em>3<\/sub><\/td>\nQuartile three<\/td>\nthe third quartile<\/td>\n<\/tr>
Descriptive Statistics<\/td>\nIQR<\/em><\/td>\ninterquartile range<\/td>\nQ<\/em>3<\/sub> \u2013 Q<\/em>1<\/sub> = IQR<\/em><\/td>\n<\/tr>
Descriptive Statistics<\/td>\nx<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nx-bar<\/td>\nsample mean<\/td>\n<\/tr>
Descriptive Statistics<\/td>\n\u03bc<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmu<\/td>\npopulation mean<\/td>\n<\/tr>
Descriptive Statistics<\/td>\ns<\/strong> sx<\/sub><\/em> sx<\/em><\/td>\ns<\/td>\nsample standard deviation<\/td>\n<\/tr>
Descriptive Statistics<\/td>\ns<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> s<\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ns squared<\/td>\nsample variance<\/td>\n<\/tr>
Descriptive Statistics<\/td>\n\u03c3<\/span><\/span><\/span><\/span><\/span><\/span> \u03c3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u03c3x<\/em><\/td>\nsigma<\/td>\npopulation standard deviation<\/td>\n<\/tr>
Descriptive Statistics<\/td>\n\u03c3<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u03c3<\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsigma squared<\/td>\npopulation variance<\/td>\n<\/tr>
Descriptive Statistics<\/td>\n\u03a3<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ncapital sigma<\/td>\nsum<\/td>\n<\/tr>
Probability Topics<\/td>\n{<\/span>}<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nbrackets<\/td>\nset notation<\/td>\n<\/tr>
Probability Topics<\/td>\nS<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nS<\/td>\nsample space<\/td>\n<\/tr>
Probability Topics<\/td>\nA<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nEvent A<\/td>\nevent A<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprobability of A<\/td>\nprobability of A occurring<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>|<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprobability of A given B<\/td>\nprob. of A occurring given B has occurred<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>\u00a0OR\u00a0<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprob. of A or B<\/td>\nprob. of A or B or both occurring<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>\u00a0AND\u00a0<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprob. of A and B<\/td>\nprob. of both A and B occurring (same time)<\/td>\n<\/tr>
Probability Topics<\/td>\nA<\/em>\u2032<\/td>\nA-prime, complement of A<\/td>\ncomplement of A, not A<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/em>(A<\/em>')<\/td>\nprob. of complement of A<\/td>\nsame<\/td>\n<\/tr>
Probability Topics<\/td>\nG<\/em>1<\/sub><\/td>\ngreen on first pick<\/td>\nsame<\/td>\n<\/tr>
Probability Topics<\/td>\nP<\/em>(G<\/em>1<\/sub>)<\/td>\nprob. of green on first pick<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nPDF<\/em><\/td>\nprob. distribution function<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nX<\/em><\/td>\nX<\/td>\nthe random variable X<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nX<\/em> ~<\/td>\nthe distribution of X<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nB<\/em><\/td>\nbinomial distribution<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nG<\/em><\/td>\ngeometric distribution<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nH<\/em><\/td>\nhypergeometric dist.<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\nP<\/em><\/td>\nPoisson dist.<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\n\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nLambda<\/td>\naverage of Poisson distribution<\/td>\n<\/tr>
Discrete Random Variables<\/td>\n<\/span>\u2265<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ngreater than or equal to<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\n<\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nless than or equal to<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\n=<\/td>\nequal to<\/td>\nsame<\/td>\n<\/tr>
Discrete Random Variables<\/td>\n\u2260<\/td>\nnot equal to<\/td>\nsame<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>)<\/td>\nf<\/em> of x<\/em><\/td>\nfunction of x<\/em><\/td>\n<\/tr>
Continuous Random Variables<\/td>\npdf<\/em><\/td>\nprob. density function<\/td>\nsame<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nU<\/em><\/td>\nuniform distribution<\/td>\nsame<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nExp<\/em><\/td>\nexponential distribution<\/td>\nsame<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nk<\/em><\/td>\nk<\/em><\/td>\ncritical value<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>) =<\/td>\nf<\/em> of x<\/em> equals<\/td>\nsame<\/td>\n<\/tr>
Continuous Random Variables<\/td>\nm<\/em><\/td>\nm<\/em><\/td>\ndecay rate (for exp. dist.)<\/td>\n<\/tr>
The Normal Distribution<\/td>\nN<\/em><\/td>\nnormal distribution<\/td>\nsame<\/td>\n<\/tr>
The Normal Distribution<\/td>\nz<\/em><\/td>\nz<\/em>-score<\/td>\nsame<\/td>\n<\/tr>
The Normal Distribution<\/td>\nZ<\/em><\/td>\nstandard normal dist.<\/td>\nsame<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\nCLT<\/em><\/td>\nCentral Limit Theorem<\/td>\nsame<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\nX<\/span>\u23af\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nX<\/em>-bar<\/td>\nthe random variable X<\/em>-bar<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03bc<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmean of X<\/em><\/td>\nthe average of X<\/em><\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03bc<\/span>x<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmean of X<\/em>-bar<\/td>\nthe average of X<\/em>-bar<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03c3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstandard deviation ofX<\/em><\/td>\nsame<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03c3<\/span>x<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstandard deviation ofX<\/em>-bar<\/td>\nsame<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03a3<\/span>X<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsum of X<\/em><\/td>\nsame<\/td>\n<\/tr>
The Central Limit Theorem<\/td>\n\u03a3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsum of x<\/em><\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nCL<\/em><\/td>\nconfidence level<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nCI<\/em><\/td>\nconfidence interval<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nEBM<\/em><\/td>\nerror bound for a mean<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nEBP<\/em><\/td>\nerror bound for a proportion<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nt<\/em><\/td>\nStudent's t<\/em>-distribution<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\ndf<\/em><\/td>\ndegrees of freedom<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\nt<\/span>\u03b1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstudent t with a<\/em>\/2 area in right tail<\/td>\nsame<\/td>\n<\/tr>
Confidence Intervals<\/td>\np<\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span>; p<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\np<\/em>-prime; p<\/em>-hat<\/td>\nsample proportion of success<\/td>\n<\/tr>
Confidence Intervals<\/td>\nq<\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span>; q<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nq<\/em>-prime; q<\/em>-hat<\/td>\nsample proportion of failure<\/td>\n<\/tr>
Hypothesis Testing<\/td>\nH<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH<\/em>-naught, H<\/em>-sub 0<\/td>\nnull hypothesis<\/td>\n<\/tr>
Hypothesis Testing<\/td>\nH<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH-a<\/em>, H<\/em>-sub a<\/em><\/td>\nalternate hypothesis<\/td>\n<\/tr>
Hypothesis Testing<\/td>\nH<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH<\/em>-1, H<\/em>-sub 1<\/td>\nalternate hypothesis<\/td>\n<\/tr>
Hypothesis Testing<\/td>\n\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nalpha<\/td>\nprobability of Type I error<\/td>\n<\/tr>
Hypothesis Testing<\/td>\n\u03b2<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nbeta<\/td>\nprobability of Type II error<\/td>\n<\/tr>
Hypothesis Testing<\/td>\nX<\/span>1<\/span><\/span>\u23af\u23af\u23af\u23af\u23af<\/span><\/span>\u2212<\/span>X<\/span>2<\/span><\/span>\u23af\u23af\u23af\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nX<\/em>1-bar minus X<\/em>2-bar<\/td>\ndifference in sample means<\/td>\n<\/tr>
Hypothesis Testing<\/td>\n\u03bc<\/span>1<\/span><\/span>\u2212<\/span>\u03bc<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmu<\/em>-1 minus mu<\/em>-2<\/td>\ndifference in population means<\/td>\n<\/tr>
Hypothesis Testing<\/td>\nP<\/span>\u2032<\/span><\/span>1<\/span><\/span>\u2212<\/span>P<\/span>\u2032<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nP<\/em>1-prime minus P<\/em>2-prime<\/td>\ndifference in sample proportions<\/td>\n<\/tr>
Hypothesis Testing<\/td>\np<\/span>1<\/span><\/span>\u2212<\/span>p<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\np<\/em>1 minus p<\/em>2<\/td>\ndifference in population proportions<\/td>\n<\/tr>
Chi-Square Distribution<\/td>\n\u03a7<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nKy<\/em>-square<\/td>\nChi-square<\/td>\n<\/tr>
Chi-Square Distribution<\/td>\nO<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nObserved<\/td>\nObserved frequency<\/td>\n<\/tr>
Chi-Square Distribution<\/td>\nE<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nExpected<\/td>\nExpected frequency<\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\ny<\/em> = a<\/em> + bx<\/em><\/td>\ny<\/em> equals a plus b-x<\/em><\/td>\nequation of a line<\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\ny<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ny<\/em>-hat<\/td>\nestimated value of y<\/em><\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\nr<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ncorrelation coefficient<\/td>\nsame<\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\n\u03b5<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nerror<\/td>\nsame<\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\nSSE<\/em><\/td>\nSum of Squared Errors<\/td>\nsame<\/td>\n<\/tr>
Linear Regression and Correlation<\/td>\n1.9s<\/em><\/td>\n1.9 times s<\/em><\/td>\ncut-off value for outliers<\/td>\n<\/tr>
F<\/em>-Distribution and ANOVA<\/td>\nF<\/em><\/td>\nF<\/em>-ratio<\/td>\nF<\/em>-ratio<\/td>\n<\/tr><\/tbody><\/table><\/section>","rendered":"
\n

English Phrases Written Mathematically<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
When the English says:<\/th>\nInterpret this as:<\/th>\n<\/tr>\n<\/thead>\n
X<\/em> is at least 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
The minimum of X<\/em> is 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is no less than 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is greater than or equal to 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is at most 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
The maximum of X<\/em> is 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is no more than 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is less than or equal to 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> does not exceed 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is greater than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is more than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> exceeds 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is less than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
There are fewer X<\/em> than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
X<\/em> is 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is equal to 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is the same as 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is not 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not equal to 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not the same as 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is different than 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n
\n

Formulas<\/h1>\n

Formula 1: Factorial<\/span>n<\/span>!<\/span>=<\/span>n<\/span>(<\/span>n<\/span>\u2212<\/span>1<\/span>)<\/span>(<\/span>n<\/span>\u2212<\/span>2<\/span>)<\/span>.<\/span>.<\/span>.<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

0<\/span>!<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 2: Combinations<\/span>(<\/span>n<\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span>n<\/span>!<\/span><\/span>(<\/span>n<\/span>\u2212<\/span>r<\/span>)<\/span>!<\/span>r<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 3: Binomial Distribution<\/span>X<\/span>~<\/span>B<\/span>(<\/span>n<\/span>,<\/span>p<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>(<\/span>n<\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>p<\/span>x<\/span><\/span>q<\/span>n<\/span>\u2212<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, for x<\/span>=<\/span>0<\/span>,<\/span>1<\/span>,<\/span>2<\/span>,<\/span>.<\/span>.<\/span>.<\/span>,<\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 4: Geometric Distribution<\/span>X<\/span>~<\/span>G<\/span>(<\/span>p<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>q<\/span>x<\/span>\u2212<\/span>1<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, for x<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>.<\/span>.<\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 5: Hypergeometric Distribution<\/span>X<\/span>~<\/span>H<\/span>(<\/span>r<\/span>,<\/span>b<\/span>,<\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>(<\/span>(<\/span>r<\/span>x<\/span><\/span>)<\/span><\/span>(<\/span>b<\/span>n<\/span>\u2212<\/span>x<\/span><\/span><\/span>)<\/span><\/span><\/span>(<\/span>r<\/span>+<\/span>b<\/span><\/span>n<\/span><\/span>)<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 6: Poisson Distribution<\/span>X<\/span>~<\/span>P<\/span>(<\/span>\u03bc<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

P<\/span>(<\/span>X<\/span>=<\/span>x<\/span>)<\/span>=<\/span>\u03bc<\/span>x<\/span><\/span>e<\/span>\u2212<\/span>\u03bc<\/span><\/span><\/span><\/span>x<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 7: Uniform Distribution<\/span>X<\/span>~<\/span>U<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>X<\/span>)<\/span>=<\/span>1<\/span>b<\/span>\u2212<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, a<\/span><<\/span>x<\/span><<\/span>b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 8: Exponential Distribution<\/span>X<\/span>~<\/span>E<\/span>x<\/span>p<\/span>(<\/span>m<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>m<\/span>e<\/span>\u2212<\/span>m<\/span>x<\/span><\/span><\/span>m<\/span>><\/span>0<\/span>,<\/span>x<\/span>\u2265<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 9: Normal Distribution<\/span>X<\/span>~<\/span>N<\/span>(<\/span>\u03bc<\/span>,<\/span>\u03c3<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>1<\/span>\u03c3<\/span>2<\/span>\u03c0<\/span><\/span>\u221a<\/span><\/span><\/span>e<\/span>\u2212<\/span>(<\/span>x<\/span>\u2212<\/span>\u03bc<\/span>)<\/span><\/span>2<\/span><\/span>2<\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> , \u2013<\/span>\u221e<\/span><<\/span>x<\/span><<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 10: Gamma Function<\/span>\u0393<\/span>(<\/span>z<\/span>)<\/span>=<\/span>\u222b<\/span><\/span><\/span><\/span><\/span>\u221e<\/span>0<\/span><\/span>x<\/span>z<\/span>\u2212<\/span>1<\/span><\/span><\/span>e<\/span>\u2212<\/span>x<\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span> z<\/span>><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0393<\/span>(<\/span>1<\/span>2<\/span><\/span>)<\/span>=<\/span>\u03c0<\/span><\/span>\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0393<\/span>(<\/span>m<\/span>+<\/span>1<\/span>)<\/span>=<\/span>m<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span> for m<\/span><\/span><\/span><\/span><\/span><\/span>, a nonnegative integer<\/p>\n

otherwise: \u0393<\/span>(<\/span>a<\/span>+<\/span>1<\/span>)<\/span>=<\/span>a<\/span>\u0393<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 11: Student’s t<\/em>-distribution<\/span>X<\/span>~<\/span>t<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>(<\/span>1<\/span>+<\/span>x<\/span>2<\/span><\/span>n<\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span>(<\/span>n<\/span>+<\/span>1<\/span>)<\/span><\/span>2<\/span><\/span><\/span>\u0393<\/span>(<\/span>n<\/span>+<\/span>1<\/span><\/span>2<\/span><\/span>)<\/span><\/span><\/span>n\u03c0<\/span><\/span>\u221a<\/span>\u0393<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

X<\/span>=<\/span>Z<\/span>Y<\/span>n<\/span><\/span><\/span>\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Z<\/span>~<\/span>N<\/span>(<\/span>0<\/span>,<\/span>1<\/span>),<\/span>Y<\/span>~<\/span>\u03a7<\/span>2<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, n<\/span><\/span><\/span><\/span><\/span><\/span> = degrees of freedom<\/span><\/span><\/span><\/span><\/span><\/p>\n

\n<\/div>\n

Formula 12: Chi-Square Distribution<\/span>X<\/span>~<\/span>\u03a7<\/span>2<\/span>d<\/span>f<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>x<\/span>n<\/span>\u2212<\/span>2<\/span><\/span>2<\/span><\/span><\/span>e<\/span>\u2212<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>2<\/span>n<\/span>2<\/span><\/span><\/span>\u0393<\/span>(<\/span>n<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, x<\/span>><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span> , n<\/span><\/span><\/span><\/span><\/span><\/span> = positive integer and degrees of freedom<\/p>\n

\n<\/div>\n

Formula 13: F Distribution<\/span>X<\/span>~<\/span>F<\/span>d<\/span>f<\/span>(<\/span>n<\/span>)<\/span>,<\/span>d<\/span>f<\/span>(<\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

d<\/span>f<\/span>(<\/span>n<\/span>)<\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>degrees of freedom for the numerator<\/span><\/span><\/p>\n

d<\/span>f<\/span>(<\/span>d<\/span>)<\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>degrees of freedom for the denominator<\/span><\/span><\/p>\n

f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>\u0393<\/span>(<\/span>u<\/span>+<\/span>v<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\u0393<\/span>(<\/span>u<\/span>2<\/span><\/span>)<\/span>\u0393<\/span>(<\/span>v<\/span>2<\/span><\/span>)<\/span><\/span><\/span>(<\/span>u<\/span>v<\/span><\/span>)<\/span><\/span>u<\/span>2<\/span><\/span><\/span><\/span>x<\/span>(<\/span>u<\/span>2<\/span><\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span>[<\/span>1<\/span>+<\/span>(<\/span>u<\/span>v<\/span><\/span>)<\/span>x<\/span>\u2212<\/span>0.5<\/span>(<\/span>u<\/span>+<\/span>v<\/span>)<\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

X<\/span>=<\/span>Y<\/span>u<\/span><\/span>W<\/span>v<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, Y<\/span><\/span><\/span><\/span><\/span><\/span>, W<\/span><\/span><\/span><\/span><\/span><\/span> are chi-square<\/p>\n<\/section>\n

\n

Symbols and Their Meanings<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Symbols and their Meanings<\/span><\/caption>\n
Chapter (1st used)<\/th>\nSymbol<\/th>\nSpoken<\/th>\nMeaning<\/th>\n<\/tr>\n<\/thead>\n
Sampling and Data<\/td>\n\u00a0\u00a0<\/span><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nThe square root of<\/td>\nsame<\/td>\n<\/tr>\n
Sampling and Data<\/td>\n\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nPi<\/td>\n3.14159\u2026 (a specific number)<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>1<\/sub><\/td>\nQuartile one<\/td>\nthe first quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>2<\/sub><\/td>\nQuartile two<\/td>\nthe second quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>3<\/sub><\/td>\nQuartile three<\/td>\nthe third quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nIQR<\/em><\/td>\ninterquartile range<\/td>\nQ<\/em>3<\/sub> \u2013 Q<\/em>1<\/sub> = IQR<\/em><\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nx<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nx-bar<\/td>\nsample mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\u03bc<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmu<\/td>\npopulation mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\ns<\/strong> sx<\/sub><\/em> sx<\/em><\/td>\ns<\/td>\nsample standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\ns<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> s<\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ns squared<\/td>\nsample variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\u03c3<\/span><\/span><\/span><\/span><\/span><\/span> \u03c3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u03c3x<\/em><\/td>\nsigma<\/td>\npopulation standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\u03c3<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u03c3<\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsigma squared<\/td>\npopulation variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\u03a3<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ncapital sigma<\/td>\nsum<\/td>\n<\/tr>\n
Probability Topics<\/td>\n{<\/span>}<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nbrackets<\/td>\nset notation<\/td>\n<\/tr>\n
Probability Topics<\/td>\nS<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nS<\/td>\nsample space<\/td>\n<\/tr>\n
Probability Topics<\/td>\nA<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nEvent A<\/td>\nevent A<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprobability of A<\/td>\nprobability of A occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>|<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprobability of A given B<\/td>\nprob. of A occurring given B has occurred<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>\u00a0OR\u00a0<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprob. of A or B<\/td>\nprob. of A or B or both occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/span>(<\/span>A<\/span>\u00a0AND\u00a0<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nprob. of A and B<\/td>\nprob. of both A and B occurring (same time)<\/td>\n<\/tr>\n
Probability Topics<\/td>\nA<\/em>\u2032<\/td>\nA-prime, complement of A<\/td>\ncomplement of A, not A<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(A<\/em>‘)<\/td>\nprob. of complement of A<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nG<\/em>1<\/sub><\/td>\ngreen on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(G<\/em>1<\/sub>)<\/td>\nprob. of green on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nPDF<\/em><\/td>\nprob. distribution function<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em><\/td>\nX<\/td>\nthe random variable X<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em> ~<\/td>\nthe distribution of X<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nB<\/em><\/td>\nbinomial distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nG<\/em><\/td>\ngeometric distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nH<\/em><\/td>\nhypergeometric dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nP<\/em><\/td>\nPoisson dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nLambda<\/td>\naverage of Poisson distribution<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n<\/span>\u2265<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ngreater than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n<\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nless than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n=<\/td>\nequal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\u2260<\/td>\nnot equal to<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>)<\/td>\nf<\/em> of x<\/em><\/td>\nfunction of x<\/em><\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\npdf<\/em><\/td>\nprob. density function<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nU<\/em><\/td>\nuniform distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nExp<\/em><\/td>\nexponential distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nk<\/em><\/td>\nk<\/em><\/td>\ncritical value<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>) =<\/td>\nf<\/em> of x<\/em> equals<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nm<\/em><\/td>\nm<\/em><\/td>\ndecay rate (for exp. dist.)<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nN<\/em><\/td>\nnormal distribution<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nz<\/em><\/td>\nz<\/em>-score<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nZ<\/em><\/td>\nstandard normal dist.<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\nCLT<\/em><\/td>\nCentral Limit Theorem<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\nX<\/span>\u23af\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nX<\/em>-bar<\/td>\nthe random variable X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03bc<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmean of X<\/em><\/td>\nthe average of X<\/em><\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03bc<\/span>x<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmean of X<\/em>-bar<\/td>\nthe average of X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03c3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstandard deviation ofX<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03c3<\/span>x<\/span>\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstandard deviation ofX<\/em>-bar<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03a3<\/span>X<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsum of X<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\u03a3<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nsum of x<\/em><\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCL<\/em><\/td>\nconfidence level<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCI<\/em><\/td>\nconfidence interval<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBM<\/em><\/td>\nerror bound for a mean<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBP<\/em><\/td>\nerror bound for a proportion<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nt<\/em><\/td>\nStudent’s t<\/em>-distribution<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\ndf<\/em><\/td>\ndegrees of freedom<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nt<\/span>\u03b1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nstudent t with a<\/em>\/2 area in right tail<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\np<\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span>; p<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\np<\/em>-prime; p<\/em>-hat<\/td>\nsample proportion of success<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nq<\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span>; q<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nq<\/em>-prime; q<\/em>-hat<\/td>\nsample proportion of failure<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\nH<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH<\/em>-naught, H<\/em>-sub 0<\/td>\nnull hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\nH<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH-a<\/em>, H<\/em>-sub a<\/em><\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\nH<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nH<\/em>-1, H<\/em>-sub 1<\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nalpha<\/td>\nprobability of Type I error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\u03b2<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nbeta<\/td>\nprobability of Type II error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\nX<\/span>1<\/span><\/span>\u23af\u23af\u23af\u23af\u23af<\/span><\/span>\u2212<\/span>X<\/span>2<\/span><\/span>\u23af\u23af\u23af\u23af\u23af<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nX<\/em>1-bar minus X<\/em>2-bar<\/td>\ndifference in sample means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\u03bc<\/span>1<\/span><\/span>\u2212<\/span>\u03bc<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nmu<\/em>-1 minus mu<\/em>-2<\/td>\ndifference in population means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\nP<\/span>\u2032<\/span><\/span>1<\/span><\/span>\u2212<\/span>P<\/span>\u2032<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nP<\/em>1-prime minus P<\/em>2-prime<\/td>\ndifference in sample proportions<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\np<\/span>1<\/span><\/span>\u2212<\/span>p<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\np<\/em>1 minus p<\/em>2<\/td>\ndifference in population proportions<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\u03a7<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nKy<\/em>-square<\/td>\nChi-square<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\nO<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nObserved<\/td>\nObserved frequency<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\nE<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nExpected<\/td>\nExpected frequency<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\ny<\/em> = a<\/em> + bx<\/em><\/td>\ny<\/em> equals a plus b-x<\/em><\/td>\nequation of a line<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\ny<\/span>\u02c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ny<\/em>-hat<\/td>\nestimated value of y<\/em><\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\nr<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ncorrelation coefficient<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\u03b5<\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nerror<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\nSSE<\/em><\/td>\nSum of Squared Errors<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n1.9s<\/em><\/td>\n1.9 times s<\/em><\/td>\ncut-off value for outliers<\/td>\n<\/tr>\n
F<\/em>-Distribution and ANOVA<\/td>\nF<\/em><\/td>\nF<\/em>-ratio<\/td>\nF<\/em>-ratio<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n\n\t\t\t
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