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I see that a lot of questions are answered here for multivariate and bivariate conditional distributions. But I did not find the proof of these equations (I need just for bivariate case).

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to get this

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I appreciate your help

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    $\begingroup$ There are plenty of proofs on this site. I can point you to stats.stackexchange.com/a/71303 because I wrote it, but I'm sure that searching will turn up others (including others in that same thread). $\endgroup$ – whuber Feb 10 '14 at 17:29
  • $\begingroup$ @whuber Thank you for the answer, Sorry for the duplicate! I did not find the one you mentioned here before asking $\endgroup$ – Fred Feb 10 '14 at 17:34