Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent and identically distributed random variables from a distribution \(F\) with \(k^{\text {th }}\) central moment given by \(\mu_{k}\). Suppose that \(\mu_{10}<\infty\). Use Theorem 8.5 to find the asymptotic distribution of \(n^{1 / 2}\left(\hat{\mu}_{3}-\mu_{3}, \hat{\mu}_{4}-\mu_{4}, \hat{\mu}_{5}-\mu_{5}ight)^{\prime}\).