15.2.34 One dimensional random variables and their characteristics

Problem: Let \( \xi_{1}, \cdots, \xi_{n} \) are independent identically distributed random variables, with finite dispersion \( \sigma^{2} \). Let's designate \[ \bar{\xi}=\frac{\xi_{1}+\cdots+\xi_{n}}{n} . \] Find the expected value of the random variable \[ \frac{1}{n-1} \sum_{k=1}^{n}\left(\xi_{k}-\bar{\xi}\right)^{2} . \]