1. Estimation of parameters

2. Maximum likelihood What has happened was most likely

3. Examples

4. Binomial distribution Observations: k successes in N Bernoulli trials

6. Poisson distribution Observations: k 1, k 2, …, k N

8. Normal distribution Observations: X 1, X 2, …,X N

11. Exponential distribution Observations: X 1, X 2, …,X N

13. Moment estimators

14. For our examples moment estimators = maximum likelihood estimators

15. Are they always the same ? No

16. Uniform distribution Cauchy distribution

17. Unbiased and biased estimators

18. Variance of estimators minimum variance estimators