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STT211Sciences3 Unitsintermediate

Probability Distribution I

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.

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120h
Study Time
13
Weeks
9h
Per Week
intermediate
Math Level
Course Keywords
Probability DistributionSet TheoryCountingRandom VariablesLimit Theorems

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Set Theory

2

Mathematics of Counting

3

Probability Theory

4

Conditional Probability

5

Discrete Random Variables

6

Continuous Random Variables

7

Normal Distribution

8

Limit Theorems

Total Topics8 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

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

Computer Based Test

Career Opportunities

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Data Analyst

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Statistician

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Risk Analyst

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Financial Analyst

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Actuary

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Industry Applications

Real-world sectors where you can apply your knowledge

FinanceInsuranceHealthcareEngineeringData Science

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Introduction

8h

Unit 1: Prerequisites

8 study 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
2

Module 1: Introduction

8h

Unit 2: Mathematics of Counting

8 study hours
  • •Study the fundamental principle of counting.
  • •Differentiate between permutations and combinations.
  • •Solve problems involving permutations of distinct and indistinguishable objects.
Week
3

Module 1: Introduction

8h

Unit 2: Mathematics of Counting

8 study 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
4

Module 2: Probability Theory

8h

Unit 1: Elementary Principle of the Theory of Probability

8 study hours
  • •Compute probabilities of events using set theory.
  • •Apply the addition law of probability.
  • •Solve problems involving conditional probability.
Week
5

Module 2: Probability Theory

8h

Unit 1: Elementary Principle of the Theory of Probability

8 study hours
  • •Apply Bayes' Theorem to solve real-world problems.
  • •Differentiate between independent and dependent events.
  • •Solve problems involving mutually exclusive and exhaustive events.
Week
6

Module 2: Probability Theory

8h

Unit 3: Discrete Random Variables

8 study 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
7

Module 2: Probability Theory

8h

Unit 3: Discrete Random Variables

8 study 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
8

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study 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
9

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study 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
10

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study 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
11

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study 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
12

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study hours
  • •Review all modules and units.
  • •Work through additional practice problems.
  • •Prepare for tutor-marked assignments.
Week
13

MODULE TWO

8h

UNIT THREE DISCRETE RANDOM VARIABLES

8 study hours
  • •Final preparation for the examination.
  • •Focus on key concepts and formulas.
  • •Review tutor-marked assignments and feedback.

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

Thoroughly review set theory and counting principles from Module 1, as they are foundational for probability calculations.

2

Practice applying Bayes' Theorem to various scenarios to master conditional probability.

3

Focus on understanding the properties and applications of different discrete and continuous random variables.

4

Create concept maps linking probability distributions to real-world examples to enhance comprehension.

5

Work through numerous practice problems from each unit, paying close attention to the assumptions and conditions required for each distribution.

6

Prioritize understanding of the central limit theorem and its applications in approximating probabilities for large samples.

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