Probability/Local Manual of Style
It is encouraged to follow this manual when editing to ensure consistency. Nevertheless, be bold when editing. |
Purpose of this book
editThe difficulty level of this book should be similar to that of first university-level probability course. In particular, measure theory and related advanced topic should 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
editNotations
editIn 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.
- CAPITAL letters (possibly with subscripts): sets [1] or random variables [2];
- small letters (possibly with subscripts): variables or elements in sets;
- : the union of and ;
- : the intersection of and ;
- : the relative complement of in
- : is a subset of ;
- : is a proper subset of ;
- : the (absolute) complement of ;
- : a universal set;
- : the cardinality of ;
- : the power set of ;
- : the binomial coefficient indexed by and ;
- : a sample space;
- : an event space;
- : the probability (function);
- : and are independent;
- : a cumulative distribution function;
- : a probability mass or probability density function;
- : the support of ;
- : the binomial distribution with independent Bernoulli trials with success probability ;
- : the Bernoulli distribution with one Bernoulli trial with success probability ;
- : the Poisson distribution with rate parameter ;
- : the geometric distribution with success probability ;
- : the negative binomial distribution (number of failures before th successes) with success probability ;
- : the hypergeometric distribution with population size containing objects of type 1, objects of another type, and objects drawn;
- : the finite discrete distribution with vector and probability vector ;
- : the discrete uniform distribution;
- : the uniform distribution over the interval ;
- [3]: the exponential distribution with rate parameter ;
- : the gamma distribution with shape parameter and rate parameter ;
- : the beta distribution with shape parameters and ;
- : the Cauchy distribution with location parameter (with scale parameter 1);
- : the normal distribution with mean and variance ;
- : the chi-squared distribution with degrees of freedom;
- : the Student's distribution with degrees of freedom;
- : the -distribution with and degrees of freedom;
- : the multinomial distribution with trials and probability vector .
- : the -dimensional multivariate normal distribution with mean vector and covariance matrix ;
- (or ): the mean of ;
- (or ): the variance of ;
- : the standard deviation of ;
- : the covariance of and ;
- (or ) : the correlation coefficient of and ;
- Bold CAPITAL letters (e.g. , and possibly with subscript): random vectors;
- Bold small letters (e.g. , and possibly with subscript): vectors;
- : the transpose of ;
- : the dot product of and .
Abbreviations
edit- 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 (stands for 'nu', possibly with subscript).
- i.i.d: independent and identically distributed;
- mgf: moment generating function;
- CLT: Central Limit Theorem.
Conventions
edit- Use title casing for subpage (called chapter) titles, and use sentence casing for section titles.
- Use LaTeX (instead of HTML) for all math-related variables, formulas, notations etc., to ensure consistency in appearance[4].
- Use <math></math> for inline math[5];
- Use <math display=block></math> for display math (i.e. formulas on its own line);
Templates
edit- Use {{nav}} as navigation template. Put two {{nav}}'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 {{colored em}} for emphasis.
- Use {{colored definition}}, {{colored proposition}}, {{colored theorem}}, {{colored remark}}, {{colored proof}}, {{colored example}}, {{colored exercise}}, {{colored corollary}} and {{colored lemma}} for writing definitions, propositions, etc. ('type declarations' for paragraphs).
- Put {{BookCat}} at the bottom of each subpage.
- ↑ usually the first few letters in alphabetical order , e.g. and , or (mnemonic for set)
- ↑ usually the last few letters in alphabetical order), e.g. and
- ↑ It is not .
- ↑ For numbers, they can be just typed out.
- ↑ This makes the symbol bigger than that using <math display=inline></math>, and thus is clearer.
- ↑ However, conventional notations should take precedenece. E.g., we should use , instead of , for mean.