Math 154a: Statistics

Tentative Outline

1. Week 1 Probability
   1. 2.1- 2.3: Sample Space, events, axioms
   2. 2.4-2.5: discrete and continuous probability
   3. 2.6 conditional probability, Bayes Theorem

2. Week 2 More Probability
   1. 2.7-2.8 Independence, independent trials
   2. 2.9 - 2.10 Combinatorial probability
   3. 2.11 hypergoemetric and binomial distributions

3. Week 3 Random Variables
   1. Holiday
   2. 3.1-3.2: Densities and distributions
   3. 3.3-3.4: joint densities and independence

4. Week 4 More Random Variables
   1. 3.7: Conditional densities
   2. 3.8: Expectation
   3. 3.9: More expectation

5. Week 5 Variance and special Distributions
   1. 3.10: variance
   2. 4.2: Poisson
   3. 4.3: Normal
6. Week 6 Exam
   1. 4.3: More Normal
   2. Review
   3. Midterm 1

7. Week 7 Estimation

   First Draft of Writing Assignment Due Friday, Feb. 21

   1. Holiday
   2. 5.1-5.3: philosophy, properties of estimators
   3. 5.4: Unbiasedness and mean squared error
8. Week 8 Estimation with the normal distribution
   1. 5.8: Maximum likelihood estimation (MLE)
   2. 7.1-7.3: Estimates assuming normality, linear combinations
   3. 7.4, 5.9: Central Limit Theorem, Confidence Intervals
9. Week 9 Confidence Intervals and Hypothesis Testing
   1. 5.9- 5.10: CI's for binomials
   2. 6.1-6.2: Hypothesis Testing
   3. 6.3: Size and Power
10. Week 10 Review
    1. Holiday
    2. Final Draft of Essays Due Wednesday, March 12
    3. Review
11. Final Exam, March 19, 8-11 am

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