Physics307L F09:Schedule/Week 13 agenda/Weighted/Derivation

Probability is

 * $$Prob(x_A) \propto \frac{1}{\sigma_A}e^{- \frac{(x_A-X)^2}{2 \sigma_A^2}}$$

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.