View source for Probability/Local Manual of Style

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{{info|It is {{colored em|encouraged}} to follow this manual when editing to ensure consistency. Nevertheless, [[wb:bold|be bold]] when editing.}}
==Purpose of this book==
The difficulty level of this book should be similar to that of {{colored em|first}} university-level probability course. 
In particular, {{colored em|measure theory}} and related advanced topic should {{colored em|not}} be included in this book. Instead, they should be included in the [[Probability Theory]] wikibook (for measure-theoretic probability), or [[Measure Theory]] wikibook (for measure theory itself).

Applications of probability can be included briefly, but are not the main focus of this wikibook.
==Some notations and abbreviations==
===Notations===
In some occasions, these notations may have different meanings compared with those stated in the following. The words explaining the meaning of the following notations in the actual content take precedence.
* {{colored em|CAPITAL}} letters (possibly with subscripts): {{colored em|sets}} <ref>usually the {{colored em|first}} few letters in alphabetical order , e.g. <math>A,B</math> and <math>C</math>, or <math>S</math> (mnemonic for set)</ref> or {{colored em|random variables}} <ref>usually the {{colored em|last}} few letters in alphabetical order), e.g. <math>X,Y</math> and <math>Z</math></ref>;
* {{colored em|small}} letters (possibly with subscripts): {{colored em|variables}} or {{colored em|elements}} in sets;
* <math>A\cup B</math>: the {{colored em|union}} of <math>A</math> and <math>B</math>; 
* <math>A\cap B</math>: the {{colored em|intersection}} of <math>A</math> and <math>B</math>; 
* <math>A\setminus B</math>: the {{colored em|relative complement}} of <math>B</math> in <math>A</math> 
* <math>A\subseteq B</math>: <math>A</math> is a {{colored em|subset}} of <math>B</math>; 
* <math>A\subsetneq B</math>: <math>A</math> is a {{colored em|proper subset}} of <math>B</math>; 
* <math>S^c</math>: the (absolute) {{colored em|complement}} of <math>S</math>;
* <math>U</math>: a {{colored em|universal}} set;
* <math>|S|</math>: the {{colored em|cardinality}} of <math>S</math>; 
* <math>\mathcal P(S)</math>: the {{colored em|power set}} of <math>S</math>; 
* <math>\binom{n}{r}</math>: the {{colored em|binomial coefficient}} indexed by <math>n</math> and <math>r</math>; 
* <math>\Omega</math>: a {{colored em|sample space}}; 
* <math>\mathcal F</math>: an {{colored em|event space}}; 
* <math>\mathbb P</math>: the {{colored em|probability }} (function); 
* <math>A\perp\!\!\!\perp B</math>: <math>A</math> and <math>B</math> are {{colored em|independent}};
* <math>F</math>: a {{colored em|cumulative distribution function}};
* <math>f</math>: a {{colored em|probability mass}} or {{colored em|probability density function}};
* <math>\operatorname{supp}(X)</math>: the {{colored em|support}} of <math>X</math>; 
* <math>\operatorname{Binom}(n,p)</math>: the {{colored em|binomial}} distribution with <math>n</math> independent Bernoulli trials with success probability <math>p</math>;
* <math>\operatorname{Ber}(p)</math>: the {{colored em|Bernoulli}} distribution with one Bernoulli trial with success probability <math>p</math>;
* <math>\operatorname{Pois}(\lambda)</math>: the {{colored em|Poisson}} distribution with rate parameter <math>\lambda</math>;
* <math>\operatorname{Geo}(p)</math>: the {{colored em|geometric}} distribution with success probability <math>p</math>;
* <math>\operatorname{NB}(k,p)</math>: the negative binomial distribution (number of failures before <math>k</math>th successes) with success probability <math>p</math>;
* <math>\operatorname{HypGeo}(N,K,n)</math>: the {{colored em|hypergeometric}} distribution with population size <math>N</math> containing <math>K</math> objects of type 1, <math>N-K</math> objects of another type, and <math>n</math> objects drawn;
* <math>\operatorname{FD}(\mathbf x,\mathbf p)</math>: the {{colored em|finite discrete}} distribution with vector <math>\mathbf x</math> and probability vector <math>\mathbf p</math>; 
* <math>\operatorname{D}\mathcal U\{x_1,\dotsc,x_n\}</math>: the {{colored em|discrete uniform}} distribution;
* <math>\mathcal{U}[a,b]</math>: the {{colored em|uniform}} distribution over the interval <math>[a,b]</math>;
* <math>\operatorname{Exp}(\lambda)</math> <ref>It is {{colored em|not}} <math>\exp(\lambda)</math>.</ref>: the {{colored em|exponential}} distribution with rate parameter <math>\lambda</math>;
* <math>\operatorname{Gamma}(\alpha,\lambda)</math>: the {{colored em|gamma}} distribution with shape parameter <math>\alpha</math> and rate parameter <math>\lambda</math>;
* <math>\operatorname{Beta}(\alpha,\beta)</math>: the {{colored em|beta}} distribution with shape parameters <math>\alpha</math> and <math>\beta</math>;
* <math>\operatorname{Cauchy}(\theta)</math>: the {{colored em|Cauchy}} distribution with location parameter <math>\theta</math> (with scale parameter 1);
* <math>\mathcal{N}(\mu,\sigma^2)</math>: the {{colored em|normal}} distribution with mean <math>\mu</math> and variance <math>\sigma^2</math>;
* <math>\chi^2_\nu</math>: the {{colored em|chi-squared}} distribution with <math>\nu</math> degrees of freedom;
* <math>t_\nu</math>: the {{colored em|Student's <math>t</math>}} distribution with <math>\nu</math> degrees of freedom;
* <math>F_{\nu_1,\nu_2}</math>: the <math>F</math>-distribution with <math>\nu_1</math> and <math>\nu_2</math> degrees of freedom;
* <math>\operatorname{Multinom}(n,\mathbf p)</math>: the {{colored em|multinomial}}  distribution with <math>n</math> trials and probability vector <math>\mathbf p</math>. 
* <math>\mathcal{N}_k(\boldsymbol\mu,\boldsymbol\Sigma)</math>: the <math>k</math>-dimensional {{colored em|multivariate normal}} distribution with mean vector <math>\boldsymbol\mu</math> and covariance matrix <math>\boldsymbol\Sigma</math>; 
* <math>\mathbb E[X]</math> (or <math>\mu_X</math>): the {{colored em|mean}} of <math>X</math>;
* <math>\operatorname{Var}(X)</math> (or <math>\sigma^2_X</math>): the {{colored em|variance}} of <math>X</math>;
* <math>\sigma_X</math>: the {{colored em|standard deviation}} of <math>X</math>; 
* <math>\operatorname{Cov}(X,Y)</math>: the {{colored em|covariance}} of <math>X</math> and <math>Y</math>;
* <math>\rho(X,Y)</math> (or <math>\rho_{XY}</math>) : the {{colored em|correlation coefficient}} of <math>X</math> and <math>Y</math>;
* '''Bold''' {{colored em|CAPITAL}} letters (e.g. <math>\mathbf X</math>, and possibly with subscript): {{colored em|random vectors}};
* '''Bold''' {{colored em|small}} letters (e.g. <math>\mathbf x</math>, and possibly with subscript): {{colored em|vectors}}; 
* <math>\mathbf x^T</math>: the {{colored em|transpose}} of <math>\mathbf x</math>;  
* <math>\mathbf x\cdot\mathbf y</math>: the {{colored em|dot product}} of <math>\mathbf x</math> and <math>\mathbf y</math>.

===Abbreviations===
* no.: number;
* r.v.: random variable;
* cdf: cumulative distribution function;
* pmf: probability mass function;
* pdf: probability density function;
* s.d.: standard deviation;
* df: degrees of freedom;
:* It is usually denoted by <math>\nu</math> (stands for 'nu', possibly with subscript). 
* i.i.d: independent and identically distributed;
* mgf: moment generating function;
* CLT: Central Limit Theorem.
==Conventions==
* Use {{colored em|title}} casing for {{colored em|subpage}} (called chapter) titles, and use {{colored em|sentence}} casing for section titles.
* Use LaTeX (instead of HTML) for {{colored em|all}} math-related variables, formulas, notations etc., to ensure consistency in appearance<ref>For numbers, they can be just typed out.</ref>.
:* Use <nowiki><math></math></nowiki> for {{colored em|inline}} math<ref>This makes the symbol bigger than that using <nowiki><math display=inline></math></nowiki>, and thus is clearer.</ref>;
:* Use <nowiki><math display=block></math></nowiki> for {{colored em|display}} math (i.e. formulas on its own line);
* Use [[help:quizzes|quizzes]] (if possible) for exercises.
* Try to use mnemonic notations (if possible). E.g., <math>S</math> for a set, <math>t</math> for time, etc. <ref>However, conventional notations should take precedenece. E.g., we should use <math>\mu</math>, instead of <math>m</math>, for mean.</ref>
==Templates==
* Use {{tl|nav}} as navigation template. Put two {{tl|nav}}'s for each subpage, one at top, one at bottom, and enclose each of them by <nowiki><noinclude></noinclude></nowiki>, so that they do not appear at the print version.
* Use {{tl|colored em}} for emphasis.
* Use {{tl|colored definition}}, {{tl|colored proposition}}, {{tl|colored theorem}}, {{tl|colored remark}}, {{tl|colored proof}}, {{tl|colored example}}, {{tl|colored exercise}}, {{tl|colored corollary}} and {{tl|colored lemma}} for writing definitions, propositions, etc. ('type declarations' for paragraphs).
* Put {{tl|BookCat}} at the bottom of each subpage.
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