Probability

Study Course Description

Course Description Statuss:Approved

Course Description Version:5.00

Study Course Accepted:07.09.2023 09:07:25

Study Course Information
Course Code:		SL_104		LQF level:		Level 7
Credit Points:		2.00		ECTS:		3.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Eva Petrošina
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		14 Baložu street, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		8	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		16
Classes (count)		4	Class Length (academic hours)		2	Total Contact Hours of Classes		8
Total Contact Hours								24
Part-Time - Semester No.1
Lectures (count)		8	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		8
Classes (count)		4	Class Length (academic hours)		2	Total Contact Hours of Classes		8
Total Contact Hours								16
Study course description
Preliminary Knowledge:
Knowledge in calculus.
Objective:
This course introduces students to probability and random variables and introduces probability with applications in order to get knowledge on fundamental probability concepts.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Combinatorial Analysis (the basic principle of counting; permutations; combinations; multinomial coefficients).			Lectures		1.00	computer room
				Classes		0.50	computer room
2	Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).			Lectures		1.00	computer room
				Classes		0.50	computer room
3	Conditional Probability and Independence (conditional probabilities; Bayes' formula; independent events).			Lectures		1.00	computer room
				Classes		0.50	computer room
4	Random Variables (discrete RVs; expectation; variance; Bernoulli and binomial RVs; the Poisson RV; sums of RVs; cumulative distribution function).			Lectures		1.00	computer room
				Classes		0.50	computer room
5	Continuous Random Variables (expectation and variance again; uniform RV; normal RV; exponential RV; functions of RV).			Lectures		1.00	computer room
				Classes		0.50	computer room
6	Jointly Distributed Random Variables (joint distribution functions; independent RVs; sums of independent RVs; conditional distributions (discrete and continuous cases); order statistics; joint distribution of functions of RVs).			Lectures		1.00	computer room
				Classes		0.50	computer room
7	Expectation (expectation of sums of RVs; moments of event counting functions; covariance, correlation, and variance of sums; conditional expectation; prediction; moment generating functions).			Lectures		1.00	computer room
				Classes		0.50	computer room
8	Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).			Lectures		1.00	computer room
				Classes		0.50	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Combinatorial Analysis (the basic principle of counting; permutations; combinations; multinomial coefficients).			Lectures		1.00	computer room
				Classes		0.50	computer room
2	Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).			Lectures		1.00	computer room
				Classes		0.50	computer room
3	Conditional Probability and Independence (conditional probabilities; Bayes' formula; independent events).			Lectures		1.00	computer room
				Classes		0.50	computer room
4	Random Variables (discrete RVs; expectation; variance; Bernoulli and binomial RVs; the Poisson RV; sums of RVs; cumulative distribution function).			Lectures		1.00	computer room
				Classes		0.50	computer room
5	Continuous Random Variables (expectation and variance again; uniform RV; normal RV; exponential RV; functions of RV).			Lectures		1.00	computer room
				Classes		0.50	computer room
6	Jointly Distributed Random Variables (joint distribution functions; independent RVs; sums of independent RVs; conditional distributions (discrete and continuous cases); order statistics; joint distribution of functions of RVs).			Lectures		1.00	computer room
				Classes		0.50	computer room
7	Expectation (expectation of sums of RVs; moments of event counting functions; covariance, correlation, and variance of sums; conditional expectation; prediction; moment generating functions).			Lectures		1.00	computer room
				Classes		0.50	computer room
8	Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).			Lectures		1.00	computer room
				Classes		0.50	computer room
Assessment
Unaided Work:
1) Literature studies on each of 8 topics of each lecture. 2) 2 homeworks on the following topics: • Combinatorial Analysis, Axioms of Probability and Conditional Probability and Independence. • Random Variables, Continuous Random Variables and Jointly Distributed Random Variables, Expectation and Limit Theorems. In order to evaluate the quality of the study course as a whole, the student must fill out the study course evaluation questionnaire on the Student Portal.
Assessment Criteria:
Assessment on the 10-point scale according to the RSU Educational Order: • 2 homeworks, each one counting 30% of the final grade; • written exam 40%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		The student will: 1) independently define event, outcome, trial, simple event, sample space and calculate the probability that an event will occur; 2) demonstrate deeper knowledge in fundamental probability concepts, including random variable, probability of an event, additive rules and conditional probability, Bayes’ theorem; 3) recognize, distinguish and use the basic statistical concepts and measures; 4) recognize and comprehend several well-known distributions.
Skills:		The student will have skills to: 1) derive probability distributions of functions of random variables; 2) derive expressions for measures such as the mean and variance of common probability distributions using calculus and algebra; 3) calculate probabilities for joint distributions including marginal and conditional probabilities; 4) develop the concept of the central limit theorem.
Competencies:		The student will be competent to: 1) to evaluate and solve problems independently; 2) prove some basic theorems of probability theory; 3) choose appropriately and apply the central limit theorem to sampling distributions.
Bibliography
No.	Reference
Required Reading
1	Ross, S. M. A First Course in Probability. 9th edition, Pearson, 2014.
Additional Reading
1	Morin, D. Probability. CreateSpace, 2016.
2	Dekking, F. M., Meester, L. E., Lopuhaä, H. P. and Kraaikamp, C. A. Modern Introduction to Probability and Statistics: Understanding Why and How. Springer, 2007.