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Assume vector $\bf{X}_k\in\mathbb{R}^N$, for all $k\in\cal{K}=\{1,2,\cdots,K\}$ are $K$ i.i.d. random variables. If each $\bf{X}_k$ is an unbiased estimator of parameter $\bf X$, then how to compute the following expression? Assume that $\mathbb{E}[\|\bf{X}_k\|]$ and $\mathbb{E}[\|\bf{X}_k\|^2]$ are known in advance.

$$\mathbb{E}[\|\frac{1}{K}\sum_{k\in\cal{K}}\bf{X}_k-\bf{X}\|^2]$$

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