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There are 6 modules in this course
The course "Foundations of Probability and Random Variables" introduces fundamental concepts in probability and random variables, essential for understanding computational methods in computer science and data science. Through five comprehensive modules, learners will explore combinatorial analysis, probability, conditional probability, and both discrete and continuous random variables. By mastering these topics, students will gain the ability to solve complex problems involving uncertainty, design probabilistic models, and apply these concepts in fields like machine learning, AI, and algorithm design.
What makes this course unique is its practical approach: students will develop hands-on proficiency in the R programming language, which is widely used in data science and statistical modeling. The course also includes real-world applications, allowing learners to bridge theoretical knowledge with practical problem-solving skills. Whether you are aiming to pursue advanced studies in machine learning or develop data-driven solutions in professional settings, this course provides the solid foundation you need to excel. Designed for learners with a background in calculus and basic programming, this course prepares you to tackle more advanced topics in computational science.
This course provides a comprehensive introduction to fundamental concepts in probability and statistics, focusing on counting principles, permutations, combinations, and multinomial coefficients. You will explore probability axioms, conditional probabilities, and Bayes’s Formula while using Venn diagrams to visualize events. The course covers random variables, including discrete and continuous types, expected values, and various probability distributions. Practical applications in R programming and data analysis tools will enhance understanding through simulations and real-world problem-solving. By the end, you will be equipped to analyze and interpret statistical data effectively.
What's included
2 readings1 plugin
Show info about module content
2 readings•Total 10 minutes
Course Overview•5 minutes
Instructor Biography - Dr. Tony Johnson•5 minutes
1 plugin•Total 4 minutes
Instructor Biography - Dr. Ian McCulloh•4 minutes
Combinatorial Analysis
Module 2•6 hours to complete
Module details
This module covers the usefulness of an effective method for counting the number of ways that things can occur. Many problems in probability theory can be solved simply by counting the number of different ways that a certain event can occur.
What's included
9 videos2 readings3 assignments1 ungraded lab
Show info about module content
9 videos•Total 116 minutes
Introduction to Data Science•20 minutes
Basic Principle of Counting•7 minutes
Generalized Principle of Counting•4 minutes
Permutations and Combinations•18 minutes
Circular Permutations•10 minutes
Combinations•19 minutes
Factorials and Identity•18 minutes
Distributing Indistinguishable Items•8 minutes
R Tutorial•13 minutes
2 readings•Total 90 minutes
Reading References•45 minutes
Reading References•45 minutes
3 assignments•Total 90 minutes
Fundamentals of Counting in Data Science•15 minutes
Mastering Combinatorial Techniques: From Combinations to R Applications•15 minutes
Combinatorial Analysis•60 minutes
1 ungraded lab•Total 60 minutes
Practice Lab: Exploring Combinatorics and Permutations Using R•60 minutes
Probability
Module 3•8 hours to complete
Module details
This module introduces the concept of the probability of an event and then shows how probabilities can be computed in certain situations.
What's included
9 videos3 readings4 assignments1 ungraded lab
Show info about module content
9 videos•Total 141 minutes
Sample Spaces•14 minutes
Events•12 minutes
Venn Diagram•10 minutes
DeMorgan Laws•11 minutes
Axioms of Probability•16 minutes
Simple Propositions•22 minutes
Equally Likely Outcomes•15 minutes
ELO Example•13 minutes
R Tutorial•29 minutes
3 readings•Total 180 minutes
Reading References•60 minutes
Reading References•60 minutes
Reading References•60 minutes
4 assignments•Total 105 minutes
Understanding Probability: Sample Spaces, Events, and Venn Diagrams•15 minutes
Foundations of Probability: DeMorgan's Laws and Axioms•15 minutes
Exploring Probability: Simple Propositions, Equally Likely Outcomes, and R Tutorial•15 minutes
Probability•60 minutes
1 ungraded lab•Total 60 minutes
Practice Lab: Understanding Probability and Combinatorics Using R•60 minutes
Conditional Probability and Independence
Module 4•10 hours to complete
Module details
This module explores one of the most important concepts in probability theory, that of conditional probability. The importance of this concept is twofold. First, you will be interested in calculating probabilities when some partial information concerning the result of an experiment is available; in such a situation, the desired probabilities are conditional. Second, even when no partial information is available, conditional probabilities can often be used to compute the desired probabilities more easily.
What's included
8 videos3 readings4 assignments1 ungraded lab
Show info about module content
8 videos•Total 73 minutes
Conditional Probability•10 minutes
Example Cond Prob•14 minutes
Reb Balls from Urn•5 minutes
Revisit Bayes Rule•11 minutes
Independence•7 minutes
Ex Medical Testing•12 minutes
Paradox of the Carnival Dice•9 minutes
Paradox of the Discrimination Lawsuit•6 minutes
3 readings•Total 360 minutes
Reading References•120 minutes
Reading References•120 minutes
Reading References•120 minutes
4 assignments•Total 105 minutes
Conditional Probability and Practical Examples•15 minutes
Bayes' Rule and Probability Independence•15 minutes
Exploring Probability Paradoxes and Real-World Applications•15 minutes
Conditional Probability and Independence•60 minutes
1 ungraded lab•Total 60 minutes
Practice Lab: COVID-19 Probability Models and Testing Scenarios in R •60 minutes
Discrete Random Variables
Module 5•14 hours to complete
Module details
This module discusses the function of outcomes rather than the actual outcomes themselves. In particular, you will examine random variables that can take on at most a countable number of possible values. You can call these types of variables, discrete random variables.
What's included
9 videos4 readings5 assignments1 ungraded lab
Show info about module content
9 videos•Total 176 minutes
Random Variables•16 minutes
R.V. Coin Toss•15 minutes
Coin Toss Proof•9 minutes
Expected Value•19 minutes
Expectation of R.V. Function•15 minutes
Variance of R.V.•13 minutes
Bernoulli R.V. and Mass Functions•43 minutes
Defective Product Example•19 minutes
R Tutorial•28 minutes
4 readings•Total 480 minutes
Reading References•120 minutes
Reading References•120 minutes
Reading References•120 minutes
Reading References•120 minutes
5 assignments•Total 120 minutes
Introduction to Random Variables and Coin Tosses•15 minutes
Understanding Expected Value and Random Variables•15 minutes
Variance and Bernoulli Random Variables•15 minutes
Analyzing Defective Products and R Tutorial•15 minutes
Discrete Random Variables•60 minutes
1 ungraded lab•Total 60 minutes
Practice Lab: Statistical Computation and Simulation Using R•60 minutes
Continuous Random Variables
Module 6•11 hours to complete
Module details
This module extends the concept of random variables where the outcomes cannot be counted. You will explore probability density functions, cumulative distribution functions, the normal distribution and other common distributions.
What's included
10 videos4 readings5 assignments1 ungraded lab
Show info about module content
10 videos•Total 118 minutes
Continuous RV•10 minutes
PDF and CDF•13 minutes
PDF and CDF Example•5 minutes
Means and Expectation•8 minutes
Uniform PDF Example•11 minutes
Cumulative Distribution Function (CDF)•11 minutes
The Normal Distribution•17 minutes
Normal Distribution Example•8 minutes
Other Distributions and the Hazard Rate•20 minutes
R Tutorial•17 minutes
4 readings•Total 360 minutes
Reading References•90 minutes
Reading References•90 minutes
Reading References•90 minutes
Reading References•90 minutes
5 assignments•Total 120 minutes
Continuous Random Variables: PDF and CDF Basics•15 minutes
Means, Expectation, and Uniform PDF Example•15 minutes
Understanding CDF and the Normal Distribution•15 minutes
Exploring Distributions, Hazard Rates, and R•15 minutes
Continuous Random Variables•60 minutes
1 ungraded lab•Total 60 minutes
Practice Lab: Statistical Simulations and Probability Modeling in R•60 minutes
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