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

[Ben Bolker]

  And Mathematica says

In[2]:= 1/Sqrt[2 Pi] Integrate[Exp[-x^2/2] Sqrt[x],{x,0,Infinity}]

                3
          Gamma[-]
                4
Out[2]= -------------
         3/4
        2    Sqrt[Pi]

(I suppose there's probably a change-of-variables trick to do this ...)

in R:

> gamma(3/4)/(2^(3/4)*sqrt(pi))
[1] 0.4110895


Ravi Varadhan wrote:
> 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 
>