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::Okay, no problem. [[User:Nijdam|Nijdam]] ([[User talk:Nijdam|talk]]) 07:08, 19 April 2013 (UTC)
== cdf notation ==
I went through and changed the notation <math>F_X(x)</math> to <math>F(x)</math> everywhere in the definition section to try to obtain notational consistency through the article, but the change was reverted by Nijdam with edit summary "Difference between cdf of X and just a cdf". But that conflicts with much notation in the article that uses F(x) for the cdf of X. In the Properties section:
:''the CDF of ''X'' will be discontinuous at the points ''x''<sub>''i''</sub> and constant in between:''
::<math>F(x) = \operatorname{P}(X\leq x) = \sum_{x_i \leq x} \operatorname{P}(X = x_i) = \sum_{x_i \leq x} p(x_i).</math>
:''If the CDF ''F'' of ''X'' is [[continuous function|continuous]], then ''X'' is a [[continuous random variable]]; if furthermore ''F'' is [[absolute continuity|absolutely continuous]], then there exists a [[Lebesgue integral|Lebesgue-integrable]] function ''f''(''x'') such that''
::<math>F(b)-F(a) = \operatorname{P}(a< X\leq b) = \int_a^b f(x)\,dx</math>
:''for all real numbers ''a'' and ''b''. The function ''f'' is equal to the [[derivative]] of ''F'' [[almost everywhere]], and it is called the [[probability density function]] of the distribution of ''X''.''
In the Examples section:
:''As an example, suppose ''X'' is [[uniform distribution (continuous)|uniformly distributed]] on the unit interval [0, 1]. Then the CDF of X is given by''
::<math>F(x) = \begin{cases}
0 &:\ x < 0\\
x &:\ 0 \le x < 1\\
1 &:\ 1 \le x.
\end{cases}</math>
In the Derived functions section:
::<math>\bar F(x) = \operatorname{P}(X > x) = 1 - F(x).</math>
In the multivariate case section:
:''for a pair of random variables ''X,Y'', the joint CDF <math>F</math> is given by''
::<math>F(x,y) = \operatorname{P}(X\leq x,Y\leq y),</math>
So we need to establish consistency of notation -- either use F<sub>X</sub> ''every'' time we mention a cdf "of X", or else never. Your thoughts? [[User:Duoduoduo|Duoduoduo]] ([[User talk:Duoduoduo|talk]]) 15:08, 17 May 2013 (UTC)
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