1
$\begingroup$

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.

$\endgroup$
3
  • $\begingroup$ Can you please clarify if the mean is the letter "o" or the number "0"? $\endgroup$
    – Ertxiem - reinstate Monica
    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. $\endgroup$
    – Tchaikovski
    Mar 14, 2019 at 11:29
  • $\begingroup$ Thanks, I will correct. $\endgroup$
    – bixiou
    Mar 14, 2019 at 12:06

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.