2-7 Minimum magnitude error estimate. Given p(x, 2), show that the Bayesian estimation that minimizes the expected value of the cost function C(x-\hat{x}) \stackrel{\Delta}{=}|x-\hat{x}| \text { yiclds } \hat{x}=x_{\text {ni

}} \text { , the median of } x \text { , defincd as } \int_{-\infty}^{I_{M}} p(x \mid z) d x=\frac{1}{2}