Alternate Sample Variance I

MediumStatistics

Let $X_1,\dots, X_n \sim N(\mu,\sigma^2)$ IID. Define

V = \dfrac{1}{2(n-1)}\sum_{i=1}^{n-1} (X_{i+1} - X_i)^2

The expected value of $V$ is a function a $\sigma^{2}$ . Compute $\mathbb{E}\left[ V \right]$ when the true value of $\sigma^{2}$ is 1.

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