1. Assume $X_{1}, X_{2}, \ldots, X_{n}$ are i.i.d. samples from $X \sim N\left(\mu, \sigma^{2} ight) $ ditribution. Calculate the constant $\mathrm{k}$ which makes $\sigma^{2}=\frac{1}{k} \sum_{i=1}^{n- 1}\left(x_{i+1}-X_{i} ight)^{2}$ be the unbiased estimation of $\sigma^{2}$. SP.VS. 808