Existence of a regular conditional distribution(rcd) implies existence of density for rcd?

Asked Aug 24 '17 at 21:21

Active Aug 25 '17 at 08:21

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Does the existence of a regular conditional distribution(rcd) imply the existence of a density for rcd? This question is motivated by the following example. The way it's written, seems to suggest so...

This other question also seems to have the answer to mine. However, it's written in a very complex way, which honestly I don't understand.

Any help would be appreciated.

edited Aug 25 '17 at 08:21

asked Aug 24 '17 at 21:21

An old man in the sea.

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No, it does not. The example in no way suggests that the density exists in general. – zhoraster Aug 25 '17 at 09:37
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@zhoraster Thanks for your comment. Could you give such an example? thanks – An old man in the sea. Aug 26 '17 at 07:46
Example: $Y$ is any random variable without density and $X$ is constant. – zhoraster Aug 26 '17 at 07:52
@zhoraster thanks for the comment. If Y, X have a joint density and X has a marginal density, then can the conditional distribution, also have one? was this the point of the example? ;) – An old man in the sea. Aug 26 '17 at 18:43
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If there is a joint density, then there is both marginal density and the conditinal density. This is the point. – zhoraster Aug 27 '17 at 06:20

Existence of a regular conditional distribution(rcd) implies existence of density for rcd?

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