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

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## Contents

- 1 See Taylor 2nd edition page 174 or Bevington 2nd edition page 58
- 2 Step 1: Probability of each measured mean, given parent distributions with same true value
- 3 Step 2: What is joint probability of getting both means?
- 4 Step 3: Principle of maximum likelihood: minimize chi-squared with respect to X
- 5 Step 4: Solve for X
- 6 Step 5: Error propagation to obtain new sigma

## 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.