Mathematical Statistics - STAT 512

12:30 PM - 2:10 PM, MTWR Carolina Coliseum 3020D, Jun 21, 2021 - Jul 29, 2021

Instructor office hours: After class each day in person or virtually
Instructor office: Carolina Coliseum 4020

Course syllabus

Lecture notes Accompanying slides Topics Corresponding section(s) of Wackerly book
STAT 511 summary sheet.pdf
Lec_00.pdf Lec_00_R_code Lec_00_slides.pdf Introduction
Lec_01.pdf Lec_01_slides.pdf Transformations of a random variable 6.2, 6.3, 6.4, 6.5
Lec_02.pdf Lec_02_slides.pdf Transformations of multiple random variables 6.5, 6.6
Lec_03.pdf Lec_03_slides.pdf Random samples, statistics, especially order statistics 6.1, 6.5, 6.7, 7.1
End exam I material
Lec_04.pdf Lec_04_slides.pdf Pivot quantities and sampling from the Normal distribution 7.2, 8.5, 8.8, 8.9
Lec_05.pdf Lec_05_R_code Lec_05_slides.pdf Parametric estimation and properties of estimators 8.1, 8.2, 8.3, 8.4
Lec_06.pdf Lec_06_R_code Lec_06_slides.pdf Large-sample properties of estimators: consistency and the WLLN 9.3
End exam II material
Lec_07.pdf Lec_07_slides.pdf
Large-sample pivot quantities and central limit theorem 7.3, 7.4, 7.5, 8.6
Lec_08.pdf Lec_08_slides.pdf
Classical two-sample results comparing means, proportions, and variances 8.6, 8.8
Lec_09.pdf Lec_09_slides.pdf
Sample size calculations 8.7
Lec_10.pdf Lec_10_slides.pdf
First principles of estimation: sufficiency and Rao-Blackwell theorem 9.4, 9.5
Lec_11.pdf Lec_11_R_code Lec_11_slides.pdf
MoMs and MLEs 9.6, 9.7
STAT_512_summary_sheet

Homework assignments Topics Due Solutions
hw_01.pdf Transformations of a single random variable, random number generation Thursday, June 24th hw_01_sol.pdf
hw_02.pdf Bivariate transformations, sums of independent rvs Tuesday, June 29th hw_02_sol.pdf
hw_03.pdf Normal pivot quantities, order statistics Tuesday, July 6th hw_03_sol.pdf
hw_04.pdf Normal pivot quantities, confidence intervals, two-sample CIs Friday, July 9th hw_04_sol.pdf
hw_05.pdf Bias and mean squared error of estimators Tuesday, July 13th hw_05_sol.pdf
hw_06.pdf Consistency of estimators, WLLN, central limit theorem Tuesday, July 20th hw_06_sol.pdf
hw_07.pdf Two-sample results, sample size calculations Thursday, July 22nd hw_07_sol.pdf
hw_08.pdf Sufficiency, best unbiased estimators Tuesday, July 27th hw_08_sol.pdf
hw_09.pdf Method of moments and maximum likelihood estimators Not to turn in. hw_09_sol.pdf

Exams Solutions
Exam_01.pdf Exam_01_sol.pdf
Exam_02.pdf Exam_02_sol.pdf

Spring 2020 exams Solutions
STAT_512_sp_2020_Exam_01.pdf STAT_512_sp_2020_Exam_01_sol.pdf
STAT_512_sp_2020_Exam_02.pdf STAT_512_sp_2020_Exam_02_sol.pdf
STAT_512_sp_2020_Final_Exam.pdf STAT_512_sp_2020_Final_Exam_sol.pdf

Sring 2018 exams Solutions
STAT_512_sp_2018_Exam_I.pdf STAT_512_sp_2018_Exam_I_sol.pdf
STAT_512_sp_2018_Exam_II.pdf STAT_512_sp_2018_Exam_II_sol.pdf
STAT_512_sp_2018_Exam_III.pdf STAT_512_sp_2018_Exam_III_sol.pdf
STAT_512_sp_2018_Final_Exam.pdf STAT_512_sp_2018_Final_Exam_sol.pdf