Statistical Inference I

2016

Professor: |
Caroline J. Klivans |

office:
182 George Street, Office 316 e-mail: Caroline_Klivans@brown.edu office hours: Tuesday 2:30-3:30 and by appointment. |

TAs: |
Andrew Kaluzny office hours: Wednesday 5:30-7 B&H 160. Friday 3-4:430 Applied Math (182 George St.) room 005. Peter Frisch office hours: Tuesday 5-6:30 Smitty B 101. Ian Alevy Office hours: Monday 1-2 and Wednesday 1-2pm Applied Math (170 Hope St.) room 217 |

Lecture: |
TTH 1:00 - 2:20, Biomed 202 |

Beginning the 2015-2016 academic year, students may opt to enroll in

Beginning the 2015-2016 academic year, APMA 1650/1655 will be offered both semesters.

Mathematical Statistics with Applications, Wackery, Mendenhall, Scheaffer. 7th Edition.

There will be weekly homework assignments due each Thursday. You are encouraged to work together but all students

If you

Homework 1 due Thursday September 22nd. Please include this cover sheet (or equivalent) with your homework.

Homework 2 due Thursday September 29th. Please include this cover sheet (or equivalent) with your homework.

Homework 3 due Thursday October 6th Please include this cover sheet (or equivalent) with your homework.

Homework 4 due Thursday October 20th Please include this cover sheet (or equivalent) with your homework.

Homework 5 due Thursday October 28th Please include this cover sheet (or equivalent) with your homework.

Homework 6 due Thursday November 3rd Please include this cover sheet (or equivalent) with your homework.

Homework 7 due Thursday November 10th Please include this cover sheet (or equivalent) with your homework.

Normal Table (To compute probabilities from the Normal distribution)

Distributions You will be given this sheet on the midterm.

Week 1: [9/8] Introduction to central ideas of statistics and probability.

Week 2: [9/13, 9/15] Definition of a Probability Space, sample space, probability distribution. Examples. Uniform distribution. Tools for counting. Products, orderings, binomial coefficients, multinomial coefficients. (Approx. textbook sections: 2.1-2.6) Conditional probability, Bayes Law, Independence (Approx. textbook sections: 2.7-2.10)

Week 3: [9/20,9/22] Theorem of Complete Probability. Independence. Additive Law, Multiplicative Law, Tree diagrams. (Approx. textbook sections: 2.7-2.10) Random variables, Binomial, Geometric pdfs. Expectation. (Approx. textbook sections: 2.11, 3.1-3.5)

Week 4: [9/27,9/29] Linearity of expectation. Indicator R.V.s (Approx. textbook sections: 3.1-3.5) Deviations from the mean: Variance. (3.3) Markov's inequality, Chebyshev's inequality , WLLN. (~3.11).

Week 5: [10/4, 10/6] Poisson distribution (3.8). Continuous probabilities. CDFs, densities. (4.1-4.3) Uniform distribution, Normal distribution, (4.4-4.6)

Week 6: Gamma, exponential multivariate distributions, Midterm.

Week 7: Multivariate, marginal and conditional distributions, independence (5.1-5.6), expected value(5.1-5.6), Covariance and correlation. (5.7)

Week 8: Covariance and correlation. (5.7) Sampling, point estimators, Bias, MSE. (8.1-8.4)

Week 9: Central Limit Theorem. Error of estimation, confidence intervals. (7.1-7.3, 8.5-8.10) Method of Moments, MLE. (9.1-9.7)

Week 10 - : Hypothesis Testing (10.1-10.6), more Hypothesis Testing (10.7-10.10), Likelihood Ratio tests (10.11)

There will be two (in-class) midterms(~35%) and a final(~35%) in addition to weekly assignments(~30%).

Midterm 1 Thursday Oct. 13th. Midterm 2 Thursday Nov. 17th. Final - to be announced by the registrar.