Timeline for Subdivide Z into $X_1,X_2$, s.t. $Z=X_1+X_2$ and ($X_1,X_2$) obey bivariate normal

9 events

when toggle format	what		by	license	comment
Nov 21, 2019 at 22:18	vote	accept	LucasMation
Nov 21, 2019 at 17:31	comment	added	LucasMation		@DilipSarwate, OP here. Thanks for the insightful explanation. Indeed I was expecting the conditional distribution to be univariate, as X2 is now a transformation of X1
Nov 21, 2019 at 17:05	history	edited	Dilip Sarwate	CC BY-SA 4.0	added 604 characters in body
Nov 21, 2019 at 17:00	history	edited	Dilip Sarwate	CC BY-SA 4.0	added 604 characters in body
Nov 21, 2019 at 16:36	comment	added	whuber♦		Thank you. I don't think it's an effective answer, though, because it reduces the problem to finding the conditional distribution of $X_1,$ which you don't specify. BTW, many people would allow that a degenerate bivariate Normal distribution is still bivariate Normal. Maintaining that distinction would unnecessarily complicate the statements of many basic results about Normal distributions. (E.g., that linear transformations of multivariate Normal variables are multivariate Normal.)
Nov 21, 2019 at 16:31	comment	added	Dilip Sarwate		@whuber Please see revised answer.
Nov 21, 2019 at 16:31	history	edited	Dilip Sarwate	CC BY-SA 4.0	added 408 characters in body
Nov 21, 2019 at 16:27	comment	added	whuber♦		This seems to answer a different question than the one in the title, which asks for some kind of "conditional" distribution.
Nov 21, 2019 at 16:25	history	answered	Dilip Sarwate	CC BY-SA 4.0