APMA 1655
Statistical Inference I
2018


Professor: Caroline J. Klivans
office: 182 George Street, Office 316
e-mail: Caroline_Klivans@brown.edu
office hours: Mondays 2-3pm and by appointment.

TAs: Erin Bugbee
office hours: Friday 10-11, Room 217, 170 Hope St. Tuesday 3-4, Location Sayles 200.

Elliot Youth
office hours: Tuesdays 4-6. Location Sayles Hall 012.

Soryan Kumar
office hours: Monday 6-8. Location 101 Thayer St, Room 116D.

Jenna Washington (GTA)
office hours: Monday and Thursday 10-11, Sayles 002.
To email any TA please use firstname_lastname@brown.edu


Lecture: MWF 11:00 - 11:50, SmithB 106



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.

APMA 1655 provides more in depth coverage of the above topics and additional material. Applied Math concentrators are encouraged to take 1655



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

Homework:
There will be weekly homework assignments. 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.




Schedule:
Below is an approximate schedule for the course.
2018: We will be using the course Canvas site for all materials. Please see the Canvas site for all homework assignments and updates.

Week 1: Introduction to central ideas of statistics and probability.
Week 2: 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)
Week 3: Conditional probability, Bayes Law, Theorem of Complete Probability. Independence. Additive Law, Multiplicative Law, Tree diagrams. (Approx. textbook sections: 2.7-2.10)
Week 4: Random variables, Binomial, Geometric pdfs. Expectation. Linearity of expectation. Indicator R.V.s (Approx. textbook sections: 2.11, 3.1-3.5)
Week 5: Deviations from the mean: Variance. (3.3) Markov's inequality, Chebyshev's inequality (~3.11). Weak Law of Large Numbers.
Midterm one covers the topics above.

Week 6: Poisson distribution (3.8). Moment generating functions. (3.9)
Markov Chains
Continuous probabilities. CDFs, densities. (4.1-4.3)
Week 7: More CDFs, densities. Uniform distribution, Normal distribution, Gamma, exponential distributions (4.4-4.6)
Week 8: Gamma, exponential distributions, Multivariate, marginal and conditional distributions, independence (5.1-5.6)
Week 9: conditional expectation (5.1-5.6) Covariance and correlation. (5.7) Sampling, point estimators, Bias, MSE. (8.1-8.4)
Week 10: Central Limit Theorem. Error of estimation, confidence intervals. (7.1-7.3, 8.5-8.10)
Week 11: Method of Moments, MLE. (9.1-9.7)
Week 12: Hypothesis Testing (10.1-10.6)
Week 13: Hypothesis Testing (10.7-10.10)
Week 14: Likelihood Ratio tests (10.11)


Grading:
There will be two midterms(~33%) and a final(~33%) in addition to weekly assignments(~33%).


Exams:
Midterm 1 Wed. Oct. 10th. Midterm 2 Nov. 14th. Final - to be announced by the registrar.