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STT311Sciences3 Unitsintermediate

Probability Distribution Ii

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.

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52h
Study Time
13
Weeks
4h
Per Week
advanced
Math Level
Course Keywords
Probability DistributionsRandom VariablesExpectationLimit TheoremsCharacteristic Functions

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Probability Spaces

2

Random Variables

3

Discrete Distributions

4

Continuous Distributions

5

Expectation

6

Limit Theorems

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

STT211

Basic Calculus

Basic Statistics

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Statistician

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Risk Analyst

Apply your skills in this growing field

Financial Analyst

Apply your skills in this growing field

Actuary

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

FinanceInsuranceHealthcareEngineeringResearch

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Probability Spaces, Measure and Distribution

4h

Unit 1: Probability Spaces, Measure and Distribution

4 study hours
  • •Understand the definition of probability space and its notation.
  • •Solve problems related to sample space and events.
Week
2

Module 2: Distribution of Random Variables Spaces

4h

Unit 2: Distribution of Random Variable Spaces

4 study hours
  • •Differentiate between discrete and continuous random variables.
  • •Solve problems related to distribution functions.
Week
3

Module 3: Expectation of Random Variables

4h

Unit 3: Expectation of Random Variables

4 study hours
  • •Calculate the expectation of random variables.
  • •Apply theorems on expectation to solve problems.
Week
4

Module 4: Limit Theorem

4h

Unit 4: Limit Theorem

4 study hours
  • •Apply Chebyshev's Inequality to estimate probabilities.
  • •Understand convergence of random variables.
Week
5

Module 1: Probability Spaces, Measure and Distribution

4h

Unit 1: Probability Spaces, Measure and Distribution

4 study hours
  • •Review probability spaces, sample spaces, and probability measures.
  • •Work through examples and exercises.
Week
6

Module 2: Distribution of Random Variables Spaces

4h

Unit 2: Distribution of Random Variable Spaces

4 study hours
  • •Practice classifying random variables.
  • •Solve problems on distribution functions for discrete and continuous variables.
Week
7

Module 3: Expectation of Random Variables

4h

Unit 3: Expectation of Random Variables

4 study hours
  • •Calculate variance and standard deviation.
  • •Apply theorems related to variance.
Week
8

Module 4: Limit Theorem

4h

Unit 4: Limit Theorem

4 study hours
  • •Apply Demovre's Theorem.
  • •Understand and apply the Central Limit Theorem.
Week
9

Module 1: Probability Spaces, Measure and Distribution

4h

Unit 1: Probability Spaces, Measure and Distribution

4 study hours
  • •Review probability spaces, sample spaces, and probability measures.
  • •Work through examples and exercises.
Week
10

Module 2: Distribution of Random Variables Spaces

4h

Unit 2: Distribution of Random Variable Spaces

4 study hours
  • •Practice classifying random variables.
  • •Solve problems on distribution functions for discrete and continuous variables.
Week
11

Module 3: Expectation of Random Variables

4h

Unit 3: Expectation of Random Variables

4 study hours
  • •Calculate variance and standard deviation.
  • •Apply theorems related to variance.
Week
12

Module 4: Limit Theorem

4h

Unit 4: Limit Theorem

4 study hours
  • •Apply Demovre's Theorem.
  • •Understand and apply the Central Limit Theorem.
Week
13

Final Revision

6h

Final Revision

6 study hours
  • •Review all Tutor Marked Assignments (TMAs)
  • •Solve additional problems from the textbook.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all definitions and theorems from each unit.

2

Practice solving problems from the textbook and TMAs.

3

Focus on understanding the assumptions and limitations of each theorem.

4

Create concept maps linking different types of distributions.

5

Practice calculating expectations, variances, and moment generating functions.

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