How can I find $E[ Z \mid Z > 0]$ for $Z \sim N(0,1)$?

Question

I don’t know the definition of $E[Z \mid Z > 0]$. I looked it up but only multi variable answers showed up.

What I tried to do is to use the definition of $E[Z]$ changing the integration limits from $0$ to infinity and multiplying the integral by $1/2$. However, I am not sure if that is the way to do it.

Answer 1

Correct but you also divide by the probability of $Z>0$ i.e. bayes rule