1TEACH ME
Explain [topic] in Probability Theory to me step by step at a [beginner / intermediate / advanced] level. Use a simple example first, then a harder one, and ask me a question to check I understood.
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Probability Theory: Random Variables, Distributions and Limit Theorems – AI Tutor-Enabled Course Book
Original price was: $24.00.$14.00Current price is: $14.00.
- AI Tutor-enabled
- Self-paced
- Intermediate → Advanced
- Modules
- 10
- Study time
- About 38 hours
- Format
- Digital course book (PDF)
- Projects
- 4 + capstone
Think clearly about uncertainty and solve probability problems step by step.
TypeNotes & books
DeliveryInstant download after payment
- Instant download after payment
- Lifetime access in My Courses
- Secure checkout
AI Tutor-Enabled Self-Paced Professional Course Book
Think clearly about uncertainty and solve probability problems step by step.
Probability Theory is a self-paced course book covering counting, conditional probability, discrete and continuous random variables, joint distributions, expectation and the limit theorems. It is ideal preparation for statistics, actuarial science, data science and quantitative finance.
Is this you?
- Counting problems feel like tricks
- Conditional probability and Bayes’ rule are confusing
- You mix up PMFs, PDFs and CDFs
- Joint distributions and covariance feel heavy
- Exam questions combine several ideas at once
- You need probability for statistics or actuarial exams
This course book is built to close exactly that gap: clear explanations, worked practice and an AI tutor that guides you instead of just giving answers.
- Learn
- Practise
- Check with your AI Tutor
- Build projects
- Get assessed
What you’ll learn in 10 practical modules
01 Counting and CombinatoricsCount outcomes without listing them.
Key concepts
- Permutations and combinations
- Multiplication principle
- Inclusion–exclusion
Sample practice
- How many 5-card hands contain exactly two aces?
- Arrange the letters of STATISTICS
02 Probability AxiomsBuild probability from first principles.
Key concepts
- Sample spaces and events
- Axioms and basic rules
- Equally likely outcomes
Sample practice
- Find P(at least one six) in four rolls
- Use complements to simplify a problem
03 Conditional Probability and BayesUpdate probabilities with new information.
Key concepts
- Conditional probability
- Law of total probability
- Bayes’ theorem
Sample practice
- A test is 95% accurate for a 1% condition: find P(condition|positive)
- Draw a probability tree
04 Discrete Random VariablesModel countable outcomes.
Key concepts
- PMFs and CDFs
- Expected value and variance
- Bernoulli, binomial, geometric and Poisson
Sample practice
- Find E[X] for a fair die
- Model arrivals with Poisson(3)
05 Continuous Random VariablesModel measurements.
Key concepts
- PDFs and CDFs
- Uniform and exponential distributions
- Normal distribution
Sample practice
- Find P(X>2) for Exponential(0.5)
- Standardise a normal variable
06 Functions of Random VariablesFind distributions of transformed variables.
Key concepts
- CDF method
- Change of variables
- Moment generating functions
Sample practice
- Find the distribution of Y=X² for X~Uniform(0,1)
- Find the MGF of a binomial
07 Joint DistributionsWork with several random variables together.
Key concepts
- Joint, marginal and conditional distributions
- Independence
- Covariance and correlation
Sample practice
- Find marginals from a joint table
- Compute Cov(X,Y)
08 Expectation and Conditional ExpectationUse expectation as a powerful tool.
Key concepts
- Linearity of expectation
- Conditional expectation
- Law of total expectation
Sample practice
- Expected number of matches in a random permutation
- Use E[E[X|Y]]
09 Limit TheoremsSee what happens with many trials.
Key concepts
- Markov and Chebyshev inequalities
- Law of large numbers
- Central limit theorem
Sample practice
- Bound P(|X−μ|≥2σ)
- Approximate a binomial with a normal
10 Introduction to Stochastic ProcessesModel randomness over time.
Key concepts
- Markov chains
- Random walks
- Poisson processes
Sample practice
- Find a two-step transition probability
- Expected waiting time in a Poisson process
Use AI as your personal tutor, not an answer machine
The course book includes ready-to-use prompts for ChatGPT, Copilot, Gemini or any capable AI assistant. Each mode makes the AI teach, guide, check or challenge you, so you build real understanding.
2GUIDE ME
I am working on this problem: [paste problem]. Do not give me the answer. Give me one hint at a time and wait for my next step.
3CHECK MY WORK
Here is my solution: [paste working]. Check each step, tell me exactly where any mistake is and why, but let me correct it myself.
4CHALLENGE ME
Give me three exam-style Probability Theory questions on [topic], getting harder each time. Wait for my answers, then mark them and explain what I missed.
5HELP ME APPLY IT
Show me how [topic] from Probability Theory is used in a real situation, then give me a small task to try it myself.
Verify before you trust
- Ask a clear, specific question
- Solve it yourself first
- Test the answer by substituting or estimating
- Check it against the worked examples in the book
- Validate with your teacher if the AI and the book disagree
Don’t just study it. Build evidence you can show.
Project 1
Medical Testing and Bayes
Analyse false positives for a diagnostic test.
Project 2
Simulation Study
Simulate dice, cards or queues and compare with theory.
Project 3
Insurance Claims Model
Model claims with Poisson and exponential distributions.
Project 4
CLT in Action
Show the central limit theorem with simulated samples.
Final capstone
Probability Problem Portfolio
Solve 20 exam-style problems across all modules with clear reasoning.
Who this course book is for
- Mathematics and statistics students
- Actuarial exam candidates
- Data science learners
- Economics and finance students
- Engineering students
- Self-learners
Where these skills lead
- Actuarial science
- Data science
- Quantitative finance
- Risk analysis
- Research
- Engineering
The course builds skills and evidence; it does not guarantee employment or exam results.
What you receive
- 10 progressive learning modules
- Learning objectives, key concepts and practice problems
- Ready-to-use AI Tutor prompts for five learning modes
- Practical projects and a capstone
- Portfolio guide, assessment rubric and completion checklist
- Instant download and lifetime access in My Courses
| Format | Digital course book (PDF) |
|---|---|
| Learning mode | Self-paced + AI Tutor |
| Level | Intermediate → Advanced |
| Study time | About 38 hours |
| Created by | NoteStore Academy |
| Certificate | Optional project and portfolio assessment |
| Licence | Personal learning use |
| Updated | November 2, 2026 |
Certificate pathway
Want a certificate? Submit your work for optional assessment by NoteStore Academy. Certificates reflect demonstrated work, so they are not issued automatically with purchase.
Module practice work20%
Projects 1–440%
Capstone project30%
Portfolio and reflection10%
Frequently asked questions
Do I need calculus?
Calculus helps for modules 5–10. Discrete topics in modules 1–4 need only algebra.
Is it useful for actuarial exams?
It covers the core probability topics tested in early actuarial exams, with exam-style practice.
Are solutions included?
Worked solutions are provided for examples, and the AI Tutor CHECK MY WORK mode helps with practice questions.
How is it different from a statistics course?
Probability is the theory behind statistics. This book focuses on models and reasoning rather than data analysis.
How do I get the course book after paying?
Your download link appears on the order confirmation page straight away, is emailed to you, and stays in My Courses in your account.
Which AI assistant can I use?
Any capable assistant works, such as ChatGPT, Microsoft Copilot or Google Gemini. The prompts are written to work with all of them.
Start today
Probability Theory: Random Variables, Distributions and Limit Theorems
Self-paced, AI Tutor-enabled and project-based. Download instantly after payment and keep it in My Courses.
Original price was: $24.00.$14.00Current price is: $14.00.
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