Probability Distribution Ii
- Sciences
- 300 level
- 3 credit units
- 79 pages
- 3 units
This course, Probability Distribution 2, builds upon foundational probability concepts. It explores probability spaces, random variables, and their distributions, including discrete and continuous types. Key topics include expectation, variance, moment generating functions, and characteristic functions. The course also covers limit theorems such as Chebyshev's inequality and the central limit theorem, providing a solid understanding of advanced probability distributions and their applications.
About this course
- Difficulty
- Intermediate
- Study hours
- 52 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- STT211
- Basic Calculus
- Basic Statistics
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of STT311, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
STT311 · UNIT 1: PROBABILITY SPACES, MEASURE AND DISTRIBUTION
This Unit Focuses an Probability spaces, probability measures and probability distribution for continuous random variables. It gives some basic definition and relevant working examples will be given to make the concept more meaningful for the learners.
What you should be able to do
- Understand probability spaces and measures
- Classify random variables and their distributions
- Calculate expectation and variance
- Apply limit theorems to solve problems
- Use moment generating functions
- Apply characteristic functions
What it prepares you for
- Statistician
- Data Analyst
- Risk Analyst
- Financial Analyst
- Actuary
- Finance
- Insurance
- Healthcare
- Engineering
- Research
- Statistical Software (e.g., R, SPSS)
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 3: Expectation of Random Variables
Unit 3: Expectation of Random Variables
Understanding the application of moment generating functions requires a strong grasp of calculus and series expansions.
- Module 4: Limit Theorem
Unit 4: Limit Theorem
The Central Limit Theorem involves abstract concepts of convergence and requires a solid understanding of statistical inference.
A suggested way through it
13 weeks, about 54 hours in total. Yours will differ.
- Week 1Module 1: Probability Spaces, Measure and Distribution
Unit 1: Probability Spaces, Measure and Distribution · 4 hours
Understand the definition of probability space and its notation.. Solve problems related to sample space and events..
- Week 2Module 2: Distribution of Random Variables Spaces
Unit 2: Distribution of Random Variable Spaces · 4 hours
Differentiate between discrete and continuous random variables.. Solve problems related to distribution functions..
- Week 3Module 3: Expectation of Random Variables
Unit 3: Expectation of Random Variables · 4 hours
Calculate the expectation of random variables.. Apply theorems on expectation to solve problems..
- Week 4Module 4: Limit Theorem
Unit 4: Limit Theorem · 4 hours
Apply Chebyshev's Inequality to estimate probabilities.. Understand convergence of random variables..
- Week 5Module 1: Probability Spaces, Measure and Distribution
Unit 1: Probability Spaces, Measure and Distribution · 4 hours
Review probability spaces, sample spaces, and probability measures.. Work through examples and exercises..
- Week 6Module 2: Distribution of Random Variables Spaces
Unit 2: Distribution of Random Variable Spaces · 4 hours
Practice classifying random variables.. Solve problems on distribution functions for discrete and continuous variables..
- Week 7Module 3: Expectation of Random Variables
Unit 3: Expectation of Random Variables · 4 hours
Calculate variance and standard deviation.. Apply theorems related to variance..
- Week 8Module 4: Limit Theorem
Unit 4: Limit Theorem · 4 hours
Apply Demovre's Theorem.. Understand and apply the Central Limit Theorem..
- Week 9Module 1: Probability Spaces, Measure and Distribution
Unit 1: Probability Spaces, Measure and Distribution · 4 hours
Review probability spaces, sample spaces, and probability measures.. Work through examples and exercises..
- Week 10Module 2: Distribution of Random Variables Spaces
Unit 2: Distribution of Random Variable Spaces · 4 hours
Practice classifying random variables.. Solve problems on distribution functions for discrete and continuous variables..
- Week 11Module 3: Expectation of Random Variables
Unit 3: Expectation of Random Variables · 4 hours
Calculate variance and standard deviation.. Apply theorems related to variance..
- Week 12Module 4: Limit Theorem
Unit 4: Limit Theorem · 4 hours
Apply Demovre's Theorem.. Understand and apply the Central Limit Theorem..
- Week 13Final Revision
Final Revision · 6 hours
Review all Tutor Marked Assignments (TMAs). Solve additional problems from the textbook..
Preparing for the exam
- Review all definitions and theorems from each unit.
- Practice solving problems from the textbook and TMAs.
- Focus on understanding the assumptions and limitations of each theorem.
- Create concept maps linking different types of distributions.
- Practice calculating expectations, variances, and moment generating functions.
Questions students ask about this course
What is STT311 about?
This course, Probability Distribution 2, builds upon foundational probability concepts. It explores probability spaces, random variables, and their distributions, including discrete and continuous types. Key topics include expectation, variance, moment generating functions, and characteristic functions. The course also covers limit theorems such as Chebyshev's inequality and the central limit theorem, providing a solid understanding of advanced probability distributions and their applications.
How many units does STT311 have?
STT311, Probability Distribution Ii, has 3 units across 1 module, over 79 pages of course material. You can read it one unit at a time.
How many credit units is STT311?
STT311 carries 3 credit units, at 300 level in Sciences.
Is STT311 hard?
STT311 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does STT311 take to study?
About 52 hours of study, spread across its 3 units.
How is STT311 assessed?
STT311 is assessed by assignments, tutor marked assessments and final examination.
What do I need before starting STT311?
STT211 Basic Calculus Basic Statistics
What can I do with STT311?
Statistician, Data Analyst, Risk Analyst, Financial Analyst and Actuary.