Physics307L F07:Schedule/Week 14 agenda/Weighted/Derivation

Probability is
(See p. 174 of Taylor)

Simplify with chi-squared short-hand

 * $$Prob(x_A, x_B) \propto \frac{1}{\sigma_A \sigma_B}e^{-\chi^2 / 2}$$
 * $$\chi^2 = \left( \frac{x_A-X}{\sigma_A}\right)^2 + \left( \frac{x_B-X}{\sigma_B}\right)^2$$

Step 4: Solve for X
obtain result on previous page.