[R] Expectation of E(x^1/2)

[Ravi Varadhan]

Chuck showed how to do this:

fn <- function(x) sqrt(x) * dnorm(x)

> integrate(fn, 0, Inf)
0.4110895 with absolute error < 4.7e-05
>

So the (almost) exact answer is  0.4110895 + 1i * 0.4110895 

Ravi.
____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Ben Bolker <bolker at ufl.edu>
Date: Sunday, April 11, 2010 1:00 am
Subject: Re: [R] Expectation of E(x^1/2)
To: r-help at stat.math.ethz.ch


>  Haneef Anver <haneef9 <at> yahoo.com> writes:
>  
>  > I am trying to find the expectation of x^1/2 where x~N(a,b) 
>  > ( Normal with mean a and variance b). 
>  > Any feedback would be highly appreciated. 
>  
>    I have no idea at the moment how to start doing
>  this analytically, but is this at all helpful?
>  
>  > mean(sqrt(complex(re=rnorm(1000000))))
>  [1] 0.4114712+0.4103866i
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.