STAT611S22019/20 – Statistical Theory and Probability
Instructor: Dr. Sallieu Kabay Samura
Email: [email protected]
Web: hostclass.courses
Course Name: Statistical Theory and Probability (4 credit hrs)
Course Code: STAT 611 (Msc.)
University: Fourah Bay College, University of Sierra Leone
Course Description
The aim of this course is to provide a strong mathematical and conceptual foundation in the methods of statistical inference. Content includes.
 Gamma and Beta density functions
 Functions of random variables (eg. Y = X^{2}, Y = (1/X), Z = X+Y, Z = ((X+Y)/(XY)), etc)
 Jacobian of transformation.
 Derivation of Chisquare , F, T, etc. distributions using the Gamma and beta functions.
 Likelihood and sufficiency, Factorization criterion, ancillarity and conditioning.
 Point estimation, bias and variance, information and efficiency.
 Minimum variance unbiased estimation, maximum likelihood estimation.
 Hypothesis tests: pure tests, significance level
 RaoBlackwell theory, RaoCramer theory, NeymanPerson theory, and uniformly most powerful tests.
 Conditioning and invariance, tests for composite hypothesis.
 Interval estimation: confidence regions and prediction regions.
 Asymptotic properties: maximum likelihood estimates, generalised likelihood ratio tests, likelihood confidence regions.
 Laws of large numbers, generating functions, characteristic functions.
 Order statistics, limiting theorems: Polya’s theorem, Slutsky’s theorem etc. central limit theorem and strong laws, convergence of empirical processes, Chebyshev’s inequality.
Course Guidelines and materials, Open/Close times
This course is built on a biweekly framework of material. Notes and class recordings will typically be posted during the week. Assignments may be completed and submitted at any time during the week they are due.
Posted course materials, including slide for the lectures, and recordings of the synchronous lectures, will remain open throughout the month. In this fashion, students who are unable to attend the lectures for technical or personal reasons, such as unexpected difficulties with information technology, personal or family illness, or the need to become a family caretaker, will have access to all the same class materials as students who attend the lectures.
Weekly Schedule:
 Week 1: Tuesday and Friday (8pm – 10pm): Gamma and Beta density functions
 Week 2: Tuesday and Friday (8pm – 10pm): Functions of random variables and Jacobian transform
 Week 3: Tuesday and Friday (8pm – 10pm): Derivation of chisquare , F, T, etc. distributions using the Gamma and beta functions.
 Week 4: Tuesday and Friday (8pm – 10pm): Likelihood and sufficiency, Factorization criterion, ancillarity and conditioning.
 Week 5: Tuesday and Friday (8pm – 10pm): Point estimation, bias and variance, information and efficiency.
 Week 6: Tuesday and Friday (8pm – 10pm): Minimum variance unbiased estimation, maximum likelihood estimation.
 Week 7: Tuesday and Friday (8pm – 10pm): Hypothesis tests: pure tests, significance level
 Week 8: Tuesday and Friday (8pm – 10pm): RaoBlackwell theory, RaoCramer theory, NeymanPerson theory, and uniformly most powerful tests.
 Week 9: Tuesday and Friday (8pm – 10pm): Conditioning and invariance, tests for composite hypothesis.
 Week 10: Tuesday and Friday (8pm – 10pm): Interval estimation: confidence regions and prediction regions.
 Week 11: Tuesday and Friday (8pm – 10pm): Asymptotic properties: maximum likelihood estimates, generalised likelihood ratio tests, likelihood confidence regions.
 Week 12: Tuesday and Friday (8pm – 10pm): Laws of large numbers, generating functions, characteristic functions.
 Week 13: Tuesday and Friday (8pm – 10pm): Order statistics, limiting theorems: Polya’s theorem, Slutsky’s theorem etc. central limit theorem and strong laws, convergence of empirical processes, Chebyshev’s inequality.
 Week 14: Tuesday and Friday (8pm – 10pm): Order statistics, limiting theorems: Polya’s theorem, Slutsky’s theorem etc. central limit theorem and strong laws, convergence of empirical processes, Chebyshev’s inequality.
 Week 15: Tuesday and Friday (8pm – 10pm): Revision
Required Materials:
Hostclass: We will use Hostclass (https://learn.hostclass.net) as a remote classroom response system. In order to gain unlimited zoom privileges, access and storage of lecture materials, lecture video recordings, online quizzes, assignment submissions and practice past exam papers, the lecturer and students are required to register and pay an access fee to use the Hostclass Virtual Classroom.
Assignments and Examination
There will be two assignments and one virtual examination at the end of the semester. The final exam will be cumulative. Assignments would be submitted electronically and within the stipulated time. Extension will not be accepted except on some special consideration duly given by Mr.Aloysius.
Please see the tentative dates for the exams in the schedule below:
Assignment 1 
Tuesday, 20^{th} April, 2021 
Due by 11.59 pm 
Assignment 2 
Wednesday, 21^{st} April, 2021 
Due by 11.59pm 
Test 1 
Tuesday, 20^{th} April, 2021 
Due by 11.59 pm 
Test 2 
Wednesday, 21^{st} April, 2021 
Due by 11.59pm 
Grading Policy
The course will be graded on the scale:
 virtual classroom attendance = 5%
 quiz = 15%
 assignment and participation =10%
 shall be based on examination = 70%
Disclaimer
The instructors have the right to make small or largescale changes to this syllabus as academically appropriate, including in response to rapid societal changes. If and when such changes occur, the instructors will make a formal announcement of the class via multiple media.
Course Features
 Lectures 15
 Quizzes 0
 Duration 50 hours
 Skill level All levels
 Language English
 Students 3
 Assessments Yes

View Course Contents (Lecture Notes and Videos)
 Week 1: Tuesday and Friday (8pm – 10pm): Gamma and Beta density functions
 Week 2: Tuesday and Friday (8pm – 10pm): Functions of random variables and Jacobian transform
 Week 3: Tuesday and Friday (8pm – 10pm): Derivation of chisquare , F, T, etc. distributions using the Gamma and beta functions.
 Week 4: Tuesday and Friday (8pm – 10pm): Likelihood and sufficiency, Factorization criterion, ancillarity and conditioning.
 Week 5: Tuesday and Friday (8pm – 10pm): Point estimation, bias and variance, information and efficiency.
 Week 6: Tuesday and Friday (8pm – 10pm): Minimum variance unbiased estimation, maximum likelihood estimation.
 Week 7: Tuesday and Friday (8pm – 10pm): Hypothesis tests: pure tests, significance level
 Week 8: Tuesday and Friday (8pm – 10pm): RaoBlackwell theory, RaoCramer theory, NeymanPerson theory, and uniformly most powerful tests.
 Week 9: Tuesday and Friday (8pm – 10pm): Conditioning and invariance, tests for composite hypothesis.
 Week 10: Tuesday and Friday (8pm – 10pm): Interval estimation: confidence regions and prediction regions.
 Week 11: Tuesday and Friday (8pm – 10pm): Asymptotic properties: maximum likelihood estimates, generalised likelihood ratio tests, likelihood confidence regions.
 Week 12: Tuesday and Friday (8pm – 10pm): Laws of large numbers, generating functions, characteristic functions.
 Week 13: Tuesday and Friday (8pm – 10pm): Order statistics, limiting theorems: Polya’s theorem, Slutsky’s theorem etc. central limit theorem and strong laws, convergence of empirical processes, Chebyshev’s inequality.
 Week 14: Tuesday and Friday (8pm – 10pm): Order statistics, limiting theorems: Polya’s theorem, Slutsky’s theorem etc. central limit theorem and strong laws, convergence of empirical processes, Chebyshev’s inequality.
 Week 15: Tuesday and Friday (8pm – 10pm): Revision