Linear Algebra and Its Applications · Problem 3.3.42

Orthogonality — Gilbert Strang

Mathematics · statistics-variance-weights

Problem

(a) Suppose you guess your professor's age, making errors

e = -2, -1, 5

with probabilities

\frac{1}{2}, \frac{1}{4}, \frac{1}{4}

. Check that the expected error

E(e)

is zero and find the variance

E(e^2)

. (b) If the professor guesses too (or tries to remember), making errors

-1, 0, 1

with probabilities

\frac{1}{8}, \frac{6}{8}, \frac{1}{8}

, what weights

w_1

and

w_2

give the reliability of your guess and the professor's guess?