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While this question can be solved using some (hand) analysis and standard calculus, I would have thought that the following code would have worked:

Clear[x, y, c];
Expectation[x \[Conditioned] x + y > c, 
  x \[Distributed] NormalDistribution[] && 
  y \[Distributed] NormalDistribution[]]

It doesn't. Is there a way to use Expectation and Conditioned for this problem?

@AlexTournev caught my silly syntactic error: One should use brackets, not &&. Thanks!

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closed as off-topic by Bob Hanlon, m_goldberg, Bill Watts, gwr, march Jan 23 at 3:56

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, m_goldberg, Bill Watts, gwr, march
If this question can be reworded to fit the rules in the help center, please edit the question.

1
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Clear[x, y, c];
Expectation[
 x \[Conditioned] x + y > c, 
 {x \[Distributed] NormalDistribution[], 
  y \[Distributed] NormalDistribution[]}]

(*

E^(-(c^2/4))/(Sqrt[\[Pi]] Erfc[c/2])

*)
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  • $\begingroup$ Well... a simple syntactic error. I hope you won't mind if I post this answer (citing you) on the source page. Thanks! $\endgroup$ – David G. Stork Jan 22 at 0:22
  • $\begingroup$ OK! You can rewrite your code. $\endgroup$ – Alex Trounev Jan 22 at 0:25

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