Assume we have two continuous Normal RV "X" and "Y". how can I show the conditional PDF f(X|Y) and f(Y|X) is Normal?

  • $\begingroup$ If the claim you refer to in your first sentence is really as you wrote it -- "any linear combination of N Normal RVs is a Normal RV" -- then it's false. Can you also clarify what you mean by "Twins Normal RVs"? $\endgroup$ – Glen_b Oct 26 '19 at 11:17
  • 1
    $\begingroup$ For example see stats.stackexchange.com/questions/189130/… and stats.stackexchange.com/questions/120861/… $\endgroup$ – Glen_b Oct 26 '19 at 11:24
  • $\begingroup$ @Glen_b I edited my Q and make it very simple. Sorry for my bad explanation. $\endgroup$ – Hossein Shahbodaghkhan Oct 26 '19 at 12:06
  • $\begingroup$ I found an answer to your question in a related thread: see the duplicate. $\endgroup$ – whuber Oct 26 '19 at 12:28