# Physics307L F08:Schedule/Week 13 agenda/Weighted/Derivation

### From OpenWetWare

## See Taylor 2nd edition page 174 or Bevington 2nd edition page 58

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

### (I.e., assume both data sets have the same "true" value, but with differing standard deviations)

### Assume Guassian distributions

### Probability is

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

### Simplify with chi-squared short-hand

## Step 3: Principle of maximum likelihood: minimize chi-squared with respect to X

## Step 4: Solve for X

obtain result on previous page.