APMA 1655
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
To email any TA please use firstname_lastname@brown.edu

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

Problem Session: Mondays 3-4pm, Starting 10/3, 170 Hope St. Room 108.


Course Description: APMA 1650 and 1655 begin an integrated first course in mathematical statistics. The first half covers probability and the last half is statistics, integrated with its probabilistic foundation. Specific topics include probability spaces, discrete and continuous random variables, methods for parameter estimation, confidence intervals, and hypothesis testing.

Beginning the 2015-2016 academic year, students may opt to enroll in APMA 1655 for more in depth coverage of the above topics. Applied Math concentrators are encouraged to take 1655

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

Trying to decide between 0650 and1650? See here.

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


Homework:
There will be weekly homework assignments due each Thursday. You are encouraged to work together but all students must independently write up their own solutions. All homeworks are due by the beginning of class unless otherwise noted. Homeworks must be turned in to the drop off boxes in the lobby of 182 George St.

Homework Policy: Late homework will generally not be accepted. If you have a serious reason for needing to turn in an assignment late, you must contact me directly. TAs can not grant homework extensions. If you cannot complete an assignment on time, turn in as much as you can. Completing the homework on time is the best way you can get the most out of the class.
At the end of the semester we will drop your lowest homework score.

Grading Policy: If there is a mistake in the grading of your assignment (points are added incorrectly, your score was misentered into the grade book) please let me know immediately.
If you disagree with the grading of your assignment then you may: copy the relevant portion of your assignment, attach a written explanation of your disagreement and turn it back in to me. I will look at the concern at the end of the semester if it will possibly affect your overall grade. Please note that small changes in homework points generally do not affect an overall grade. Given the large size of the course, this policy allows for a better use of time by the staff.


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.

2016 Schedule:
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)

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


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