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Question

Problem 5.2 (b)​

(b) Show that the covariance of the distribution p^(x)\hat{p}(x) is

Σ^=covp^(x)=H+1n∑i=1n(xi−μ^)(xi−μ^)T,(5.9)\hat{\Sigma} = \text{cov}_{\hat{p}}(x) = H + \frac{1}{n} \sum_{i=1}^n (x_i - \hat{\mu})(x_i - \hat{\mu})^T, \tag{5.9}

where the second term on the right hand side is the sample covariance.