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

## Step 1: Probability of each measured mean, given parent distributions with same true value

### Probability is

(See p. 174 of Taylor)

## Step 2: What is joint probability of getting both means?

### Simplify with chi-squared short-hand

${\displaystyle Prob(x_{A},x_{B})\propto {\frac {1}{\sigma _{A}\sigma _{B}}}e^{-\chi ^{2}/2}}$
${\displaystyle \chi ^{2}=\left({\frac {x_{A}-X}{\sigma _{A}}}\right)^{2}+\left({\frac {x_{B}-X}{\sigma _{B}}}\right)^{2}}$

## Step 4: Solve for X

obtain result on previous page.