let $a\in \mathbb{R}$ and let X and Y be independent normally distributed random variables, with mean $0$ and respective variances $\sigma^2_X$ and $\sigma^2_Y$. Can we express $$P(X+Y<a\,|\,X<a)$$ with a simple formula (say elementary functions + erf)?

This question is related to this more general one, which hasn't been answered.

  • $\begingroup$ Can you please clarify if the mean is the letter "o" or the number "0"? $\endgroup$ Mar 14, 2019 at 10:44
  • $\begingroup$ Just a small remark on your terminology: I think you mean that X and Y are normally distributed random variables. $\endgroup$ Mar 14, 2019 at 11:29
  • $\begingroup$ Thanks, I will correct. $\endgroup$
    – bixiou
    Mar 14, 2019 at 12:06


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