Probability Distribution I
- Sciences
- 200 level
- 3 credit units
- 204 pages
- 8 units
This course introduces probability distributions. It covers prerequisites such as set theory, algebra, and calculus. Key topics include mathematics of counting, permutations, combinations, and partitioning. Students will learn about elementary probability theory, conditional probability, Bayes' theorem, and independence. The course also explores discrete random variables, Bernoulli, binomial, geometric, Poisson, and multinomial distributions. Finally, it examines continuous random variables, normal, exponential, gamma, and chi-square distributions, along with limit theorems.
About this course
- Difficulty
- Intermediate
- Study hours
- 120 hours
- Maths
- Intermediate
- Content
- Theoretical, problem solving
- Practical work
- No
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of STT211, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
STT211 · UNIT 1: PREREQUISITES
A set will be denoted by capital letters or symbols such as X,Y,A,B,….. and its elements will be denoted by lower case letters x, y, a,b,…..
What you should be able to do
- Apply set theory to solve probability problems.
- Calculate permutations and combinations.
- Compute probabilities using various approaches.
- Apply Bayes' Theorem to solve conditional probability problems.
- Identify and work with discrete and continuous random variables.
- Apply the central limit theorem to approximate probabilities.
What it prepares you for
- Data Analyst
- Statistician
- Risk Analyst
- Financial Analyst
- Actuary
- Finance
- Insurance
- Healthcare
- Engineering
- Data Science
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 1: Introduction
Unit 1: Prerequisites
The manipulation of sets and their properties, such as De Morgan's Laws, requires abstract reasoning and a solid understanding of logical operations, which can be challenging for students new to the topic.
- Module 2: Probability Theory
Unit 1: Elementary Principle of the Theory of Probability
Bayes' Theorem involves conditional probabilities and requires careful application to ensure the correct events are conditioned upon each other, which can be confusing.
A suggested way through it
13 weeks, about 104 hours in total. Yours will differ.
- Week 1Module 1: Introduction
Unit 1: Prerequisites · 8 hours
Review the definitions of sets, subsets, unions, and intersections.. Practice De Morgan's Law problems.. Solve problems involving series, exponential series, and gamma functions..
- Week 2Module 1: Introduction
Unit 2: Mathematics of Counting · 8 hours
Study the fundamental principle of counting.. Differentiate between permutations and combinations.. Solve problems involving permutations of distinct and indistinguishable objects..
- Week 3Module 1: Introduction
Unit 2: Mathematics of Counting · 8 hours
Practice calculating probabilities using relative frequency and classical approaches.. Solve exercise problems related to even, prime, and odd numbers.. Apply the first and second laws of counting to various scenarios..
- Week 4Module 2: Probability Theory
Unit 1: Elementary Principle of the Theory of Probability · 8 hours
Compute probabilities of events using set theory.. Apply the addition law of probability.. Solve problems involving conditional probability..
- Week 5Module 2: Probability Theory
Unit 1: Elementary Principle of the Theory of Probability · 8 hours
Apply Bayes' Theorem to solve real-world problems.. Differentiate between independent and dependent events.. Solve problems involving mutually exclusive and exhaustive events..
- Week 6Module 2: Probability Theory
Unit 3: Discrete Random Variables · 8 hours
Define discrete random variables and their probability density functions.. Calculate probabilities for Bernoulli and Binomial random variables.. Solve problems involving Poisson, uniform, geometric, and negative binomial distributions..
- Week 7Module 2: Probability Theory
Unit 3: Discrete Random Variables · 8 hours
Compute the expected value and variance of discrete random variables.. Apply properties of expectations and variances.. Use probability generating functions to calculate moments..
- Week 8MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Understand the concept of continuous random variables and their probability density functions.. Calculate probabilities for normal, exponential, gamma, and chi-square distributions.. Apply the central limit theorem to approximate probabilities..
- Week 9MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Compute the expected value and variance of continuous random variables.. Apply properties of expectations and variances.. Solve problems involving symmetric probability density functions..
- Week 10MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Define jointly distributed random variables and their joint probability density functions.. Calculate marginal and conditional probability density functions.. Determine if random variables are independent and compute their covariance..
- Week 11MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Apply the central limit theorem to approximate probabilities.. Understand the law of large numbers and its implications.. Solve problems involving sums and products of random variables..
- Week 12MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Review all modules and units.. Work through additional practice problems.. Prepare for tutor-marked assignments..
- Week 13MODULE TWO
UNIT THREE DISCRETE RANDOM VARIABLES · 8 hours
Final preparation for the examination.. Focus on key concepts and formulas.. Review tutor-marked assignments and feedback..
Preparing for the exam
- Thoroughly review set theory and counting principles from Module 1, as they are foundational for probability calculations.
- Practice applying Bayes' Theorem to various scenarios to master conditional probability.
- Focus on understanding the properties and applications of different discrete and continuous random variables.
- Create concept maps linking probability distributions to real-world examples to enhance comprehension.
- Work through numerous practice problems from each unit, paying close attention to the assumptions and conditions required for each distribution.
- Prioritize understanding of the central limit theorem and its applications in approximating probabilities for large samples.
Questions students ask about this course
What is STT211 about?
This course introduces probability distributions. It covers prerequisites such as set theory, algebra, and calculus. Key topics include mathematics of counting, permutations, combinations, and partitioning. Students will learn about elementary probability theory, conditional probability, Bayes' theorem, and independence. The course also explores discrete random variables, Bernoulli, binomial, geometric, Poisson, and multinomial distributions. Finally, it examines continuous random variables, normal, exponential, gamma, and chi-square distributions, along with limit theorems.
How many units does STT211 have?
STT211, Probability Distribution I, has 8 units across 4 modules, over 204 pages of course material. You can read it one unit at a time.
How many credit units is STT211?
STT211 carries 3 credit units, at 200 level in Sciences.
Is STT211 hard?
STT211 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical and problem solving work.
How long does STT211 take to study?
About 120 hours of study, spread across its 8 units.
How is STT211 assessed?
STT211 is assessed by assignments, tutor marked assessments and final examination.
What can I do with STT211?
Data Analyst, Statistician, Risk Analyst, Financial Analyst and Actuary.