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- Full Lecture 1
- Full Lecture 10
- Full Lecture 11
- Full Lecture 12
- Full Lecture 13
- Full Lecture 14
- Full Lecture 15
- Full Lecture 16
- Full Lecture 17
- Full Lecture 18
- Full Lecture 2
- Full Lecture 3
- Full Lecture 4
- Full Lecture 5
- Full Lecture 6
- Full Lecture 7
- Full Lecture 8
- Full Lecture 9
- Graduate Level: Intro to Probability and Statistics
- Lecture 1. A) Sample Space
- Lecture 1. B) Probability Function
- Lecture 1. C) Domain of Probability Function
- Lecture 1. D) Probability Space
- Lecture 1. E) More on Probability Functions
- Lecture 1. F) Random Variables
- Lecture 10. A) Finding UMVU Estimators
- Lecture 10. B) Complete Statistic
- Lecture 10. C) Cramer-Rao Lower Bound
- Lecture 11. A) Hypothesis Testing
- Lecture 11. B) Testing Procedure
- Lecture 11. C) Variation on a Theme
- Lecture 11. D) Testing Errors
- Lecture 11. E) Power Function
- Lecture 11. F) Example 1
- Lecture 11. G) Setting the Critical Value
- Lecture 12. A) Statistical Tests
- Lecture 12. B) Likelihood-Ratio Test
- Lecture 12. C) Lagrange Multiplier Test
- Lecture 12. D) Wald Test
- Lecture 12. E) Example: LRT
- Lecture 12. F) Test Equivalence
- Lecture 12. G) Equivalence Between LRT and LM Tests
- Lecture 12. H) Equivalence Between LRT and Wald Tests
- Lecture 12. I) Optimal Tests
- Lecture 12. J) Neyman-Pearson Lemma
- Lecture 13. A) Test Optimality (cont.)
- Lecture 13. B) Example: Normal
- Lecture 13. C) Karlin-Rubin Theorem
- Lecture 13. D) 2-sided Tests and Unbiased Tests
- Lecture 13. E) p-value
- Lecture 13. F) Some Notes
- Lecture 13. G) Interval Estimation/Confidence Intervals
- Lecture 14. A) Convergence
- Lecture 14. B) Law of Large Numbers
- Lecture 14. C) Convergence in Distribution
- Lecture 14. D) Slutsky’s Theorem
- Lecture 14. E) Central Limit Theorem
- Lecture 14. F) Delta Method
- Lecture 14. G) Somewhat Pedantic Remark on Notation
- Lecture 15. A) Asymptotic Properties of ML Estimators
- Lecture 15. B) Some Implications
- Lecture 15. C) Example: Hypothesis Test
- Lecture 15. D) Example: Exponential Distribution
- Lecture 15. E) Multiple Parameters
- Lecture 16. A) Bayesian Inference
- Lecture 16. B) Example: Coin Tossing
- Lecture 16. C) A More General Example
- Lecture 16. D) Conjugate Priors
- Lecture 16. E) Normal Distribution
- Lecture 16. F) "Counterexample"
- Lecture 16. G) Multiple Observations
- Lecture 16. H) Theorem: Berstein von-Mises
- Lecture 17. A) Ordinary Least Squares
- Lecture 17. B) Normal Linear Model
- Lecture 17. C) Asymptotic Properties of OLS
- Lecture 17. D) Bootstrapping
- Lecture 18. A) Multicollinearity
- Lecture 18. B) Partitioned Regression
- Lecture 18. C) Gauss-Markov Theorem
- Lecture 2. A) Random Variables (cont.)
- Lecture 2. B) Leibniz Rule
- Lecture 2. B) Leibniz Rule II
- Lecture 2. C) Transformations of Random Variables
- Lecture 3. A) Expected Value
- Lecture 3. B) Moments
- Lecture 3. C) Moment Generating Function
- Lecture 4. A) Distributions
- Lecture 4. B) Bernoulli
- Lecture 4. C) Binomial
- Lecture 4. D) Poisson
- Lecture 4. E) Uniform
- Lecture 4. F) Gamma
- Lecture 4. G) Normal
- Lecture 4. H) Dirac delta function
- Lecture 5. A) Families of Distributions
- Lecture 5. B) Chebychev's Inequality
- Lecture 5. C) Multiple Random Variables
- Lecture 6. A) Multiple Random Variables (cont.)
- Lecture 6. B) Conditional PMF/PDF
- Lecture 6. C) Conditional Moments
- Lecture 6. D) Law of Iterated Expectations
- Lecture 6. E) Conditional Variance Identity
- Lecture 6. F) Covariance and Correlation
- Lecture 6. G) Some Inequalities
- Lecture 7. A) Random Sample
- Lecture 7. B) Statistics
- Lecture 7. C) Order Statistics
- Lecture 7. D) Statistical Inference
- Lecture 8. A) Point Estimation
- Lecture 8. B) Method of Moments
- Lecture 8. C) Maximum Likelihood
- Lecture 9. A) Point Estimation (cont.)
- Lecture 9. B) Evaluating Estimators
- Lecture 9. C) Minimum Variance Estimators
- Lecture 9. D) Sufficient Statistics
- Lecture 9. E) Rao-Blackwell
- Lecture 9. F) Factorization Theorem
- Significant Statistics
