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

### From OpenWetWare

## Contents |

## 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

(See p. 174 of Taylor)

## 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.