Linear Algebra and Its Applications · Problem 3.3.39

Orthogonality — Gilbert Strang

Mathematics · weighted-least-squares

Problem

From

m

independent measurements

b_1, \ldots, b_m

of your pulse rate, weighted by

w_1, \ldots, w_m

, what is the weighted average that replaces equation (9)? It is the best estimate when the statistical variances are

\sigma_i^2 \equiv 1/w_i^2