Talk:Conditional probability distribution

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Mid	This article has been rated as Mid-priority on the project's priority scale.

Statistics Mid‑importance

	This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles
Mid	This article has been rated as Mid-importance on the importance scale.

Conditional Density doesn't have a page

Can I link "Conditional Density" to this page

of course; maybe directly to the case of continuous distributions? 132.169.4.223 (talk) 15:20, 28 June 2017 (UTC)[reply]

Split up article?

Can we split up the article into some subheadings like "Independence" and "Likelihood Function"? It seems to be a massive paragraph that you have to read to find what you want. Thoughts?daviddoria (talk) 18:47, 11 September 2008 (UTC)[reply]

Notation

In the discrete case we write $P(X=x)$ for the probability of the event {X=x} and introduce a probability function $p_{X}(x)=P(X=x)$ . In analogy: $P(X=x|Y=y)$ for the probability of the event {X=x} given the event {Y=y} and the corresponding probability function $p_{X}(x|Y=y)=P(X=x|Y=y)$ .

In the continuous case, the corresponding term for the probability function is the density: $f_{X}(x)$ . In analogy we write for the conditional density, given the event {Y=y}: $f_{X}(x|Y=y)$ . We have to consider that the event {Y=y} is short for {ω∈Ω|Y(ω)=y}. It best has to be kept as a unit, symbolizing the event.Nijdam (talk) 22:32, 22 January 2010 (UTC)[reply]

In the article

P(Y=y|X=x)

is said to be the PMF, but is it not just a probability value? Isn't the PMF

P(Y|X=x)

which is defined over the variable

Y

and not for a realization of it? 87.140.23.204 (talk) 16:17, 27 September 2024 (UTC)[reply]

Relation to independence

Isn't the result that is being referred in fact an "if and only if"-result? If so it should at least be mentioned. — Preceding unsigned comment added by Superpronker (talk • contribs) 14:47, 22 December 2011 (UTC)[reply]

Yes, you are right. Now it is so formulated. But still, the formulation is not perfect. Boris Tsirelson (talk) 15:36, 22 December 2011 (UTC)[reply]

Conditional Cumulative Distribution

Hello I was wondering if conditional CDF should get a subsection. The below source mentions that: $C_{1|2}(u_{1},u_{2})=Pr\left[U_{2}<u_{2}|U_{1}=u_{1}\right]={\frac {\partial C_{\theta }\left(u_{1},u_{2}\right)}{\partial u_{1}}}$

Source - (http://www.caee.utexas.edu/prof/bhat/ABSTRACTS/Supp_material.pdf) references Nelsen, 2006; pg 41. -Mouse7mouse9 20:33, 17 May 2013 (UTC) — Preceding unsigned comment added by Mouse7mouse9 (talk • contribs)

Actual formal definition

The measure-theoretic definition seems to attempt to define a conditional distribution from... a conditional distribution! This should be improved. 132.169.4.223 (talk) 15:20, 28 June 2017 (UTC)[reply]

No. Rather, it defines conditional distribution from conditional expectation. Boris Tsirelson (talk) 18:57, 28 June 2017 (UTC)[reply]

Confusing

The way this article is structured confuses more than it enlightens. We get a nice illustration of what a conditional expectation is for a bivariate continuous distribution. But the definition before (for which the illustration is supposed to serve) does not even allow for events with probability zero that are described in the illustration. Also, the Borel-Kolmogorov paradox is not an issue if all you have is that definition. Moreover, this definition is not even useful for basic applications as the only event it speaks of is X=x (for which it usually cannot be applied). What about X>=X for example? --178.197.229.22 (talk) 06:47, 8 March 2018 (UTC)[reply]

Yes, but this is the situation. On one hand, conditioning on events of probability zero is generally problematic. On the other hand, the conditional density is most useful in applications. You ask what about X>=x. Well, here the condition being of non-zero probability, just use Conditional probability#Conditioning on an event:

P(A|B)={\tfrac {P(A\cap B)}{P(B)}}

(integrating the joint density when needed). Boris Tsirelson (talk) 07:48, 8 March 2018 (UTC)[reply]