When i read the book 《Statistical Inference》. I could not solve a proof showed that $\frac{\sum_{i=1}^{k}n_i{(\overline{Y_i} - \overline{\overline{Y}})^2}}{k-1}$ is unbiased estimate of $σ{^2}$. I added the Expectation of $\overline{Y_i}$ and $\overline{\overline{Y}}$ to this equation, but unfortunately the last reduced equation did not show that it is the unbiased estimate of $σ{^2}$. The reason might be the method of solving this question .
Are there any other methods to solve this question? I really look forward for your answer!
