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Textbook
- Probability and Statistics, Fourth Edition, Addison Wesley (2012)
Homework:
- Hw1 (with solutions) (assigned on Friday February 2nd, due on Friday February 16th).
- Hw2 (with solutions) (assigned on Friday March 2nd, due on Monday March 19th).
- Hw3 (with solutions) (awith solutionssigned on Friday April 16th, due on day April 30th)
Instructions: Print out the homework, write down the solutions on it and staple it before you turn it in. Make sure that your solutions are correct, nicely written and well explained. Show you work, write each step of your reasonings.
Suggested Problems:
- Chapter 7: 1, 3, 5, 7 p 384, 3, 4, 5, 6 p 393/394, 3, 4, 7, 9, 12, 17, 19 p 405-407, 5, 9, 10, 13 p 416/417, 3, 4, 6, 7, 9, 11 p425/426, 2 p 441.
- Chapter 8: 3, 5, 7 p 468/469, 1, 11 p 472/473, 7, 9 p 479, 2 p 484, 1, 4, 5, 11 p 512/513.
- Chapter 9: 1, 2, 3, 9, 13, 15 548/549, 1, 4, 6, 7, 11 p 558/559, 1, 2, 4, 5, 7, 10, 13 p 585/586, 4, 5, 6, 9 p 596.
Final:
- Monday May 7th 12:00pm-2:00pm
- Program: The final exam will be all encompassing. Review sections 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3, 8.5, 8.7, 9.1, 9.2, 9.5, 9.6. Open notes, open book.
Schedule
| Date | Section Covered | Problems Solved | Reading assignments |
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| 8 January | Review continuous random variables, expected value, variance | | sections 4.2 (p 217-224), properties of variance (p 228-234) |
| 10 January | Review of Moments, generating functions, important continuous distributions, independence, covariance | | properties of m.g.f (p 237-239) |
| 12 January | Review Cumulative Distribution Functions, convergence in distribution, Central Limit Theorem | | sections 6.3 (p 360-370) |
| 17 January | Application of CLT, Beginning 7.1: Notion of Statistical Inference, statistical Models, Obs. RV, Hypo. Obs. RV, Parameter Space | | |
| 19 January | End 7.2: Notion of Statistical Inference, statistical Models, general classes of inference, Observational vs. Experimental studies | | |
| 22 January | Beginning 7.2: prior distributions, posterior distributions | | Parameters as RV (p 382-384) |
| 24 January | 7.2: prior distributions, posterior distributions | 7 p 394 | |
| 26 January | End 7.2: likelihood functions, sequential observations | 8 p 394 | Example 7.2.8, summary p. 392/393 |
| 29 January | Beginning 7.3: Conjugate prior distributions | 2 p 405 | |
| 31 January | 7.3: Conjugate prior distributions | 15 p 406 | |
| 2 February | 7.3: Conjugate prior distribution, improper priors. Beginning 7.4: Estimators, estimates | 21 p 406 | |
| 5 February | 7.4: Loss functions, Expected Loss, Bayesian estimators/estimates, Squared Error Loss Function | | |
| 7 February | 7.4: Bayesian estimators/estimates, Squared Error Loss Function | 3 p 416 | |
| 9 February | 7.4: Consistency of Bayesian estimators | 1 p 416, 7 p 416 | |
| 12 February | 7.5: Maximum Likelihood Estimators MLE) | | |
| 14 February | 7.5: MLE | 5, 11 p 427 | |
| 16 February | 7.6: Invariance of M.L.E | 3 p 441 | Limitations of M.L.E p422-425 |
| 21 February | 7.6: M.L.E of an arbitrary function, Invariance | 5 p 441 | |
| 26 February | 8.1: Sampling distribution of a statistics | | |
| 28 February | 8.1: Sampling distribution of a statistics | 1, 9 p 468 | |
| 2 March | 8.2: Chi-square Distribution | 7 p 472 | |
| 5 March | 8.2: Chi-square Distribution | 2, 9 p 472 | |
| 7 March | 8.3: Joint distribution of Sample Mean and Sample Variance | | Proof Thm. 8.3.1 p 476--478 |
| 9 March | 8.4: t-distributions | 1, 5 p 479, 3 p 484 | |
| 12 March | 8.7: Unbiased estimators, Bias, Mean Square Error | | |
| 14 March | 8.t: Unibiased estimator of the variance | 2, 3 p 512 | |
| 16 March | 8.7: Consistency of unbiased estimators | 6, 7 p 513 | Limitations of unbiased estimators p 511/512 |
| 19 March | 8.5: Confidence intervals | | |
| 21 March | 8.5: Confidence intervals | 5 p 494 | |
| 2 April | 9.1: Hypotheses testing, null and alternative hypotheses, simple and composite hypotheses, critical region | | |
| 4 April | 9.1: Test statistic, rejection region, power function | 5 p 548 | |
| 6 April | 9.1: Type I/II error, significance level, size of a test | | |
| 9 April | 9.1: Type I/II error, significance level, size of a test | 6 p 548 | |
| 11 April | 9.1: Make a test have a specific significance level, p-values | 8 p 548 | Examples 9.1.8, 9.1.9 |
| 13 April | 9.1: p-values, Confidence sets | 10, 18 p 548/549 | p 540--543 |
| 16 April | 9.2: Simple Hypotheses testing | 3 p 558 | |
| 18 April | 9.2: Nayman-Pearson Lemma | 5 p 558 | |
| 20 April | 9.2: Nayman-Pearson Lemma | 9 p 558 | |
| 23 April | 9.5: t-test | | |
| 25 April | 9.5: t-test | 3 p585 | |
| 27 April | 9.5: t-test, p-values, non-central t-distributions | 11 p 586 | Example 9.5.5 p 579 |
| 29 April | 9.5: t-test, testing two-sided alternatives | 15 p 587 | Proof Thm 9.5.2 p 578 |
| 2 Mai | 9.6: Comparing means of two normal distributions | 3 p 596 | |
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