Veidlapa Nr. M-3 (8)
Study Course Description
Probability
Course Code
SL_104
Branch of Science
Mathematics
ECTS
3.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Ilze Balode
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
14 Baložu street, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
This course introduces students to probability and random variables and introduces probability with applications in order to get knowledge on fundamental probability concepts.
Preliminary Knowledge
Knowledge in calculus.
Learning Outcomes
Knowledge
1.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
1.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.
Competences
1.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.
Assessment
Individual work
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Title
|
% from total grade
|
Grade
|
|---|---|---|
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1.
Individual 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.
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Examination
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Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
10 points
|
|
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%. |
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Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Combinatorial Analysis (the basic principle of counting; permutations; combinations; multinomial coefficients).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Conditional Probability and Independence (conditional probabilities; Bayes' formula; independent events).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Random Variables (discrete RVs; expectation; variance; Bernoulli and binomial RVs; the Poisson RV; sums of RVs; cumulative distribution function).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Random Variables (discrete RVs; expectation; variance; Bernoulli and binomial RVs; the Poisson RV; sums of RVs; cumulative distribution function).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Continuous Random Variables (expectation and variance again; uniform RV; normal RV; exponential RV; functions of RV).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
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).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Expectation (expectation of sums of RVs; moments of event counting functions; covariance, correlation, and variance of sums; conditional expectation; prediction; moment generating functions).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Expectation (expectation of sums of RVs; moments of event counting functions; covariance, correlation, and variance of sums; conditional expectation; prediction; moment generating functions).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).
|
Total ECTS (Creditpoints):
3.00
Contact hours:
24 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Combinatorial Analysis (the basic principle of counting; permutations; combinations; multinomial coefficients).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Axioms of Probability (sample spaces and events; axioms of probability; sample spaces having equally likely outcomes).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Conditional Probability and Independence (conditional probabilities; Bayes' formula; independent events).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Conditional Probability and Independence (conditional probabilities; Bayes' formula; independent events).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Random Variables (discrete RVs; expectation; variance; Bernoulli and binomial RVs; the Poisson RV; sums of RVs; cumulative distribution function).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Continuous Random Variables (expectation and variance again; uniform RV; normal RV; exponential RV; functions of RV).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Continuous Random Variables (expectation and variance again; uniform RV; normal RV; exponential RV; functions of RV).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
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).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Expectation (expectation of sums of RVs; moments of event counting functions; covariance, correlation, and variance of sums; conditional expectation; prediction; moment generating functions).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Limit Theorems (Chebyshev's inequality; weak law of large numbers; central limit theorem; strong law of large numbers).
|
Total ECTS (Creditpoints):
3.00
Contact hours:
16 Academic Hours
Final Examination:
Exam (Written)
Bibliography
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.