Suppose that you wish to pick one number to characterize a set of data x1,x2,...,xN . Prove that the mean x, defined by x = 1 N N j=1 xj , minimizes the mean square error Q = 1 N N j=1 (xj - x) 2....

Suppose that you wish to pick one number to characterize a set of data x1,x2,...,xN . Prove that the mean x, defined by x = 1 N N j=1 xj , minimizes the mean square error Q = 1 N N j=1 (xj - x) 2. Problem 3 Derive Eqs. 11.5. Problem 4 Suppose that the experimental values y(xj ) are exactly equal to the calculated values plus random noise for each data point: y(xj ) = ycalc(xj )+nj . What is Q?