Probability/Local Manual of Style

Purpose of this book

The difficulty level of this book should be similar to that of Template:Colored em university-level probability course. In particular, Template:Colored em and related advanced topic should Template:Colored em 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.

• Template:Colored em letters (possibly with subscripts): Template:Colored em or Template:Colored em ;
• Template:Colored em letters (possibly with subscripts): Template:Colored em or Template:Colored em in sets;
• $A\cup B$: the Template:Colored em of $A$ and $B$;
• $A\cap B$: the Template:Colored em of $A$ and $B$;
• $A\setminus B$: the Template:Colored em of $B$ in $A$
• $A\subseteq B$: $A$ is a Template:Colored em of $B$;
• $A⊊B$: $A$ is a Template:Colored em of $B$;
• $S^c$: the (absolute) Template:Colored em of $S$;
• $U$: a Template:Colored em set;
• $|S|$: the Template:Colored em of $S$;
• $𝒫(S)$: the Template:Colored em of $S$;
• $(\genfrac{}{}{0ex}{}{n}{r})$: the Template:Colored em indexed by $n$ and $r$;
• $\mathrm{\Omega }$: a Template:Colored em;
• $ℱ$: an Template:Colored em;
• $\mathbb{P}$: the Template:Colored em (function);
• $A\perp \perp B$: $A$ and $B$ are Template:Colored em;
• $F$: a Template:Colored em;
• $f$: a Template:Colored em or Template:Colored em;
• $\mathrm{supp}(X)$: the Template:Colored em of $X$;
• $\mathrm{Binom}(n,p)$: the Template:Colored em distribution with $n$ independent Bernoulli trials with success probability $p$;
• $\mathrm{Ber}(p)$: the Template:Colored em distribution with one Bernoulli trial with success probability $p$;
• $\mathrm{Pois}(\lambda )$: the Template:Colored em distribution with rate parameter $\lambda$;
• $\mathrm{Geo}(p)$: the Template:Colored em distribution with success probability $p$;
• $\mathrm{NB}(k,p)$: the negative binomial distribution (number of failures before $k$th successes) with success probability $p$;
• $\mathrm{HypGeo}(N,K,n)$: the Template:Colored em distribution with population size $N$ containing $K$ objects of type 1, $N-K$ objects of another type, and $n$ objects drawn;
• $\mathrm{FD}(𝐱,𝐩)$: the Template:Colored em distribution with vector $𝐱$ and probability vector $𝐩$;
• $\mathrm{D}𝒰\{x_1,\dots ,x_n\}$: the Template:Colored em distribution;
• $𝒰[a,b]$: the Template:Colored em distribution over the interval $[a,b]$;
• $\mathrm{Exp}(\lambda )$ : the Template:Colored em distribution with rate parameter $\lambda$;
• $\mathrm{Gamma}(\alpha ,\lambda )$: the Template:Colored em distribution with shape parameter $\alpha$ and rate parameter $\lambda$;
• $\mathrm{Beta}(\alpha ,\beta )$: the Template:Colored em distribution with shape parameters $\alpha$ and $\beta$;
• $\mathrm{Cauchy}(\theta )$: the Template:Colored em distribution with location parameter $\theta$ (with scale parameter 1);
• $𝒩(\mu ,{\sigma }^2)$: the Template:Colored em distribution with mean $\mu$ and variance ${\sigma }^2$;
• ${\chi }_{\nu }^2$: the Template:Colored em distribution with $\nu$ degrees of freedom;
• $t_{\nu }$: the Template:Colored em distribution with $\nu$ degrees of freedom;
• $F_{{\nu }_1,{\nu }_2}$: the $F$-distribution with ${\nu }_1$ and ${\nu }_2$ degrees of freedom;
• $\mathrm{Multinom}(n,𝐩)$: the Template:Colored em distribution with $n$ trials and probability vector $𝐩$.
• ${𝒩}_k(\mathit{\mu },\mathrm{\Sigma })$: the $k$-dimensional Template:Colored em distribution with mean vector $\mathit{\mu }$ and covariance matrix $\mathrm{\Sigma }$;
• $𝔼[X]$ (or ${\mu }_X$): the Template:Colored em of $X$;
• $\mathrm{Var}(X)$ (or ${\sigma }_X^2$): the Template:Colored em of $X$;
• ${\sigma }_X$: the Template:Colored em of $X$;
• $\mathrm{Cov}(X,Y)$: the Template:Colored em of $X$ and $Y$;
• $\rho (X,Y)$ (or ${\rho }_{XY}$) : the Template:Colored em of $X$ and $Y$;
• Bold Template:Colored em letters (e.g. $𝐗$, and possibly with subscript): Template:Colored em;
• Bold Template:Colored em letters (e.g. $𝐱$, and possibly with subscript): Template:Colored em;
• ${𝐱}^T$: the Template:Colored em of $𝐱$;
• $𝐱\cdot 𝐲$: the Template:Colored em of $𝐱$ and $𝐲$.

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 $\nu$ (stands for 'nu', possibly with subscript).

• i.i.d: independent and identically distributed;
• mgf: moment generating function;
• CLT: Central Limit Theorem.

Conventions

• Use Template:Colored em casing for Template:Colored em (called chapter) titles, and use Template:Colored em casing for section titles.
• Use LaTeX (instead of HTML) for Template:Colored em math-related variables, formulas, notations etc., to ensure consistency in appearance.

• Use <math></math> for Template:Colored em math;
• Use <math display=block></math> for Template:Colored em math (i.e. formulas on its own line);

• Use quizzes (if possible) for exercises.
• Try to use mnemonic notations (if possible). E.g., $S$ for a set, $t$ for time, etc.

Templates

• Use Template:Tl as navigation template. Put two Template:Tl's for each subpage, one at top, one at bottom, and enclose each of them by <noinclude></noinclude>, so that they do not appear at the print version.
• Use Template:Tl for emphasis.
• Use Template:Tl, Template:Tl, Template:Tl, Template:Tl, Template:Tl, Template:Tl, Template:Tl, Template:Tl and Template:Tl for writing definitions, propositions, etc. ('type declarations' for paragraphs).
• Put Template:Tl at the bottom of each subpage.