Question

Let  $x_{1},...,x_{n}$ be numeric observations or a random variable. Find the value $u$ that minimizes the function $g(u)= \sum_{i=1}^{n} (x_{i}-u)^{2}$ .

Help me to solve this problem, thankyou very much.

Answer 1

9. gru): 12,-42 (04-03 + (0-132 +---+ (225-452 = CU-x ² + (U-22² + – – 4 (U-x)? -> gu)- 2(-8) +2(U-23) + -- -- +2(4-Xn) 2[nu - (95+Xz+-+%)] g'(W) 0 => us (94+7+---+2) = X Also grlu)=ano - uix is point of minima i glu) is minimum at u=5 = 1/(X + 2+ + 2)