Talk:Conditional probability distribution

This article is rated C-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Mathematics Mid‑priority 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 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 Mid This article has been rated as Mid-importance on the importance scale.

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

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

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

In the continuous case, the corresponding term for the probability function is the density: ${\displaystyle f_{X}(x)}$. In analogy we write for the conditional density, given the event {Y=y}: ${\displaystyle f_{X}(x|Y=y)}$. 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 ${\displaystyle P(Y=y|X=x)}$ is said to be the PMF, but is it not just a probability value? Isn't the PMF ${\displaystyle P(Y|X=x)}$ which is defined over the variable ${\displaystyle Y}$ and not for a realization of it? 87.140.23.204 (talk) 16:17, 27 September 2024 (UTC)Reply

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

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

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)

Presently there are quite a few articles that attempt to deal with conditional probability (and expectation), with varing levels of quality:

• conditioning (probability)
• conditional probability
• conditional probability distribution
• regular conditional probability
• conditional expectation

etc. It seems quite arbitrary which contains what. I think (some of) these should be reorganized, unified, and probably combined and merged into fewer articles. 80.98.239.192 (talk) 13:06, 3 November 2013 (UTC)Reply

I think that, at least, conditional probability and conditional probability distribution should be merged. regular conditional probability is technical and should be simply linked too. 132.169.4.223 (talk) 15:11, 28 June 2017 (UTC)Reply

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

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: ${\displaystyle P(A|B)={\tfrac {P(A\cap B)}{P(B)}}}$ (integrating the joint density when needed). Boris Tsirelson (talk) 07:48, 8 March 2018 (UTC)Reply