Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables following a mixture of two NORMAL distributions, with a density given by \(f(x)=\frac{1}{2} \phi(x-\zeta)+\frac{1}{2} \phi(x+\zeta)\) where \(\theta\) is a positive real number. Compute the asymptotic relative efficiency of the sample mean relative to the sample median as an estimator of the mean of this density. Comment on the role that the parameter \(\zeta\) has on the efficiency.