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1. (5 points) Let {=1, x2, and be a set of points in d-dimensional space. Suppose we wish to produce a single point estimate ss € Rd that minimizes the mean squared-error: 1 - + ||:r2 - + + - n Find a closed form expression for H and prove that your answer is correct. 2. (10 points) Not all norms behave the same; for instance, the of a vector can be dramatically different from the E2-norm, especially in high dimensions. Prove the following norm inequalities for d-dimensional vectors, starting from the definitions provided in class and lecture notes. (Use any algebraic technique/result you like, as long as you cite it.) a. s = b. ||.z-||1 =

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