Notation in probability and statistics: Difference between revisions

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*[[Cumulative distribution function]]s (cdfs) are denoted by uppercase letters, e.g. <math>F(x)</math>, or <math>F_X(x)</math>.

* [[Survival function]]s or complementary cumulative distribution functions are often denoted by placing an [[overbar]] over the symbol for the cumulative:<math>\overline{F}(x) =1-F(x)</math>, or denoted as <math>S(x)</math>,

*In particular, the pdf of the [[standard normal distribution]] is denoted by &phi;<math display="inline">\varphi(''z'')</math>, and its cdf by <math display="inline">\Phi(z)</math>&Phi;(''z'').

*Some common operators:

:* <math display="inline">\mathrm{E}[''X'']</math> : [[expected value]] of ''X''

:* <math display="inline">\mathrm{var}[''X'']</math> : [[variance]] of ''X''

:* <math display="inline">\mathrm{cov}[''X'', ''Y'']</math> : [[covariance]] of ''X'' and ''Y''

* X is independent of Y is often written <math>X \perp Y</math> or <math>X \perp\!\!\!\perp Y</math>, and X is independent of Y given W is often written

:<math>X \perp\!\!\!\perp Y \,|\, W </math> or