Re: expected value of a normal variable with integrate()

[Sundar Dorai-Raj <sundar.dorai-raj@PDF.COM>]

You need to rescale the density to integrate to one.

What you have below only integrates to 0.5. Try

integrate(function(x) 2 * x * dnorm(x), -Inf, 0)

Regards,
Sundar

Agin.Patrick@hydro.qc.ca wrote:

> Hi,
>
> Could anyone tell me why the two following expressions don't give the 
> same result:
> integrate(function(x) x*dnorm(x),-Inf,0) equals -0.3989
> and
> tmp <- rnorm(1000000); mean(tmp[tmp<0]) approximately equals -0.79 (two 
> times -0.3989)
> I noticed that -0.3989 is the result of mean(pmin(0,tmp)), the mean of 
> all the normal deviates with a cap of zero.
> If I'm interested in the expected value of all the negatives under the 
> standard normal, the good result seems to be -0.79. Am I wrong? Why the 
> integrate() expression above doesn't give this number?
> Thank you,
> Patrick
>
> P.S. I'm using S-Plus 4.5 on Windows XP.