Let X1,X2,…∼i.i.d.X . The distribution of X depends on a positive parameter θ , which is a function of the mean μ , i.e θ=g(μ) . You estimate θ by the estimator θˆ=g(X¯¯¯¯n) .

Question

For which function g can the delta method be applied? Remember that θ>0 .
(Choose all that apply.)

1. g(x)=x^3
2.g(x)=sqrt(x)
3.g(x)=ln(x)
4.g(x)={x if x≤1, 2x−1 if x>1
5.g(x)=1/(x−1)