# Thread: expected value of a normally distributed variable

1. ## expected value of a normally distributed variable

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)?

2. Originally Posted by minivan15
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)?
Apply the ideas found in this link: Conditional Expectation

3. In general, let X be any continuous random variable.

Then $E[X|a

4. The X is a rv, not a variable of integration...

Originally Posted by Random Variable
In general, let X be any continuous random variable.

Then $E[X|a

5. 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.

6. 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.

7. Originally Posted by matheagle
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.
I apologize. I thought you were talking directly to me.

But yes, it could cause confusion.

8. so, just to make sure I have this...

the expected value of a std normal variable X, given X is between -2 and 1, is about -.229 (can someone verify this answer?)

9. Originally Posted by minivan15
so, just to make sure I have this...

the expected value of a std normal variable X, given X is between -2 and 1, is about -.229 (can someone verify this answer?)
$E[X|-2

yep