Hey...I've been thinking about this problem all day, and can't seem to come up with an exact answer.
consider a standard normally distributed random variable, say X. What is the expected value of X, given it is between two values (say 1 and -2)?
I stated that X is a random variable. And of course I meant to capitalize the X in the denominator. P(a<x<b) has no meaning. And there is nothing wrong with the way I wrote it. The denominator is a number.
I know you think I'm incredibly stupid, but give me some credit. Sheesh.
The comment was not for you, but for the poster.
The probability could be in or out of the integral, but with it inside and being lower case as with the x in the numerator it is misleading.
It could easily be interpreted as part of the integrand.
And I do not think you're stupid at all.