Problem 1C The mean as a "least squares" estimate Suppose we play the following guessing game. You pick a number from the list x1, 22, . .., In, and ask me to guess what it is. My strategy is to guess that the value is some constant c no matter what you pick. Thus for every i in the range 1 through n, the amount of error that I make with my strategy is xi - c. Define the mean squared error of my strategy to be 1 msec ( xi - c ) 2. n i=1 Show that the value of c that minimizes msec is c = M, and that msey = 02