uestion 3 e want to show that r is the argument that solves

uestion 3: e want to show that r is the argument that solves min m) a) For n 2, write explicitly 1 ai m)2. (3 points) b) What is the FCC for minimizing the expression you found in a with respect to m? (3 points c) What value of m solves the FOC you found in b)? Is it ar? (3 points)

Solution

Question 3.

a.

Here,

Sum (xi - m)^2 , i = 1 to 2 = (x1 - m)^2 + (x2 - m)^2

= x1^2 - 2 x1 m + m^2 + x2^2 - 2 x2 m + m^2

= x1^2 + x2^2 - 2m (x1 + x2) + 2m^2 [ANSWER]

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