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Probability: Basic Concepts & Discrete Random Variables




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Overview

 

Our capacity to collect and store data has exponentially increased, but deriving information from data from a scientific perspective requires a foundational knowledge of probability.

Are you interested in a career in the emerging data science field, or as an actuarial scientist? Or want better to understand statistical theory and mathematical modeling?

In this statistics and data analysis course, we will provide an introduction to mathematical probability to help meet your career goals in the exciting new areas becoming known as information science.

In this course, we will first introduce basic probability concepts and rules, including Bayes theorem, probability mass functions and CDFs, joint distributions and expected values.

Then we will discuss a few important probability distribution models with discrete random variables, including Bernoulli and Binomial distributions, Geometric distribution, Negative Binomial distribution, Poisson distribution, Hypergeometric distribution and discrete uniform distribution.

To continue learning about probability, enroll in Probability: Distribution Models & Continuous Random Variables, which covers continuous distribution models, central limit theorem and more.

 

What you'll learn

  • Basic probability concepts and rules
  • Some of the most widely used probability models with discrete random variables
  • How probability models work in practical problems

 

Module Author

Syllabus/Suggested Schedule

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Unit 1: Sample Space and Probability

 

Introduction to basic concepts, such as outcomes, events, sample spaces, and probability.

 

  • PurdueX 416 1A About
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  • Unit 1: Outcomes, Events, and Sample Spaces definitions
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  • Unit 1: Dice example
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  • Unit 1: Coin flip example
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  • Unit 1: DeMorgan's First Law
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  • Unit 1: DeMorgan's Second Law
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  • Unit 1: How many events
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  • Unit 1: Sample spaces
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  • Unit 1: Probability rules
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  • Unit 1: Probability of empty set
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  • Unit 1: Union of finitely many events
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  • Unit 1: Equally likely outcomes
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  • Unit 1: More equally likely outcomes
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  • Unit 1: Examples
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  • Unit 1: Setminus and partition
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  • Unit 1: Inclusion/Exclusion
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Unit 2: Independent Events, Conditional Probability and Bayes’ Theorem

 

Introduction to independent events, conditional probability and Bayes’ Theorem with examples

 

  • Unit 2: Independent events
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  • Unit 2: Independence / disjointness
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  • Unit 2: Independence of collections
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  • Unit 2: Examples / good vs bad trials
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  • Unit 2: Something good before something bad
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  • Unit 2: Conditional probability
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  • Unit 2: Independence
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  • Unit 2: Dice example
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  • Unit 2: Coin example
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  • Unit 2: Card example
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  • Unit 2: Distributive laws
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  • Unit 2: Conditional probability laws
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  • Unit 2: Symmetry examples
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  • Unit 2: Another coin example
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  • Unit 2: Bayes' Theorem
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  • Unit 2: Example of Bayes' Theorem
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  • Unit 2: Bayes' Theorem v2
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  • Unit 2: Example of Bayes' Theorem v2
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  • Unit 2: Bayes' Theorem v3
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  • Unit 2: Example of Bayes' Theorem v3
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  • Unit 2: Bayes' Theorem v4
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  • Unit 2: Probability of an intersection
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Unit 3: Random Variables

 

Random variables, probability mass functions and CDFs, joint distributions

 

  • Unit 3: prob0701
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  • Unit 3: prob0702
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  • Unit 3: prob0703
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  • Unit 3: prob0704
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  • Unit 3: prob0705
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  • Unit 3: prob0706
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  • Unit 3: prob0707
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  • Unit 3: prob0708
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  • Unit 3: prob0801
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  • Unit 3: prob0802
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  • Unit 3: prob0803
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  • Unit 3: prob0804
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  • Unit 3: prob0805
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  • Unit 3: prob0806
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  • Unit 3: prob0807
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  • Unit 3: prob0808
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  • Unit 3: prob0901
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  • Unit 3: prob0902
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  • Unit 3: prob0903
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  • Unit 3: prob0904
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  • Unit 3: prob0905
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  • Unit 3: prob0906
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  • Unit 3: prob0907
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  • Unit 3: prob0908
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Unit 4: Expected Values

 

In this unit, we will discuss expected values of discrete random variables, sum of random variables and functions of random variables with lots of examples.

 

  • Unit 4: prob1001
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  • Unit 4: prob1002
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  • Unit 4: prob1003
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  • Unit 4: prob1004
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  • Unit 4: prob1005
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  • Unit 4: prob1006
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  • Unit 4: prob1007
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  • Unit 4: prob1101
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  • Unit 4: prob1102
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  • Unit 4: prob1103
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  • Unit 4: prob1104
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  • Unit 4: prob1105
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  • Unit 4: prob1201
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  • Unit 4: prob1202
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  • Unit 4: prob1203
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  • Unit 4: prob1204
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  • Unit 4: prob1205
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  • Unit 4: prob1206
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Unit 5: Models of Discrete Random Variables I

 

Bernoulli and Binomial random variables; Geometric random variables; Negative Binomial random variables

 

  • Unit 5: prob1401
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  • Unit 5: prob1402
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  • Unit 5: prob1403
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  • Unit 5: prob1501
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  • Unit 5: prob1502
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  • Unit 5: prob1503
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  • Unit 5: prob1504
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  • Unit 5: prob1505
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  • Unit 5: prob1506
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  • Unit 5: prob1601
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  • Unit 5: prob1602
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  • Unit 5: prob1603
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  • Unit 5: prob1604
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  • Unit 5: prob1605
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  • Unit 5: prob1606
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  • Unit 5: prob1607
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  • Unit 5: prob1701
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  • Unit 5: prob1702
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  • Unit 5: prob1703
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  • Unit 5: prob1704
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  • Unit 5: prob1705
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  • Unit 5: prob1706
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Unit 6: Models of Discrete Random Variables II

 

Poisson random variables; Hypergeometric random variables; discrete uniform random variables and counting

 

  • Unit 6: prob1801
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  • Unit 6: prob1802
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  • Unit 6: prob1803
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  • Unit 6: prob1804
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  • Unit 6: prob1805
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  • Unit 6: prob1806
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  • Unit 6: prob1901
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  • Unit 6: prob1902
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  • Unit 6: prob1903
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  • Unit 6: prob1904
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  • Unit 6: prob1905
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  • Unit 6: prob1906
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  • Unit 6: prob2001
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  • Unit 6: prob2201
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  • Unit 6: prob2202
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  • Unit 6: prob2203
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  • Unit 6: prob2204
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  • Unit 6: prob2205
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  • Unit 6: prob2206
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