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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?

Hossein Shahbodaghkhan
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  • 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"? – Glen_b Oct 26 '19 at 11:17
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    For example see https://stats.stackexchange.com/questions/189130/is-joint-normality-a-necessary-condition-for-the-sum-of-normal-random-variables and https://stats.stackexchange.com/questions/120861/example-of-two-correlated-normal-variables-whose-sum-is-not-normal – Glen_b Oct 26 '19 at 11:24
  • @Glen_b I edited my Q and make it very simple. Sorry for my bad explanation. – Hossein Shahbodaghkhan Oct 26 '19 at 12:06
  • I found an answer to your question in a related thread: see the duplicate. – whuber Oct 26 '19 at 12:28

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