I thank those people who have responded to the question on the variance of x^.

I don't believe that it is useful to use a taylor series expansion. A taylor series is intended to approximate a complex function with a polynomial.

The taylor series expansion of x^2 is only useful if you go to the second order term; in which case the taylor series expansion of x^2 is x^2 - and so it is for any other polynomial (terms above the second order term equal zero because higher order derivatives equal zero).

However I still don't know the answer to the problem but I am more than happy to assume that x is a normally distributed random variable.

Any other help will be appreciated.

Regards Patrick