Taylor Series Approximations

[Cookie]

Hi i'm wondering if anyone knows how to approximate the variance using a taylor series expansion. I have worked out how to approximate the mean with a taylor series but have not been able to figure out how to approximate the Variance. for example how would i approximate Var(w^1/3).

[BGM]

You can take a look at wiki
http://en.wikipedia.org/wiki/Delta_method
http://en.wikipedia.org/wiki/Taylor_expansions_for_the_moments_of_functions_of_random_variables

[Mean Joe]

I think you can "reduce" the Taylor approx. for the variance into the Taylor approx. for the mean, as Var(w^1/3) = E[ (w^1/3)^2] - E^2[w^1/3]
Think of E[ (w^1/3)^2] as the mean of the random variable (w^1/3)^2, i.e. w^2/3.
And E^2[w^1/3] as the squared mean of w^1/3.