What is E[X|Y>c] where Y=X+Z, and X, Z are normally distributed rvs?

Asked Nov 03 '19 at 05:55

Active Nov 03 '19 at 09:35

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Suppose X, Z are normally distributed random variables and independent ($X$ follows $N(\mu,\sigma^{2})$ and $Z$ follows $N(0,\sigma_{z}^{2})$), and that Y=X+Z.

What is E[X|Y>c], where c is just a constant - how do you derive this?

edited Nov 03 '19 at 09:35

Xi'an

105,342

asked Nov 03 '19 at 05:55

CuriousCat

Are X and Z independent? If not are they bivariate normal and if so what is the correlation between them? – Michael R. Chernick Nov 03 '19 at 06:10
yes X Z are independent – CuriousCat Nov 03 '19 at 06:11
Are they standard normal? If not, what are the means and variances of X and Z? – gunes Nov 03 '19 at 06:24
ideally as generic as possible. let's say $X$ follows $N(\mu,\sigma^2)$ and $Z$ follows $N(0,\sigma_{z}^2)$ – CuriousCat Nov 03 '19 at 06:26
https://stats.stackexchange.com/questions/356023/expectation-of-truncated-normal/357176#357176 – Glen_b Nov 03 '19 at 08:28
Please add the self-study tag and read the associated wiki page for advices on how to ask a self-study question on this forum. – Xi'an Nov 03 '19 at 09:33

What is E[X|Y>c] where Y=X+Z, and X, Z are normally distributed rvs?

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