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In diesem Kurs gibt es 6 Module
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.
Das ist alles enthalten
2 Lektüren1 Plug-in
Infos zu Modulinhalt anzeigen
2 Lektüren•Insgesamt 10 Minuten
Course Overview•5 Minuten
Instructor Biography - Dr. Tony Johnson•5 Minuten
1 Plug-in•Insgesamt 4 Minuten
Instructor Biography - Dr. Ian McCulloh•4 Minuten
Combinatorial Analysis
Modul 2•6 Stunden abzuschließen
Moduldetails
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.
Das ist alles enthalten
9 Videos2 Lektüren3 Aufgaben1 Unbewertetes Labor
Infos zu Modulinhalt anzeigen
9 Videos•Insgesamt 116 Minuten
Introduction to Data Science•20 Minuten
Basic Principle of Counting•7 Minuten
Generalized Principle of Counting•4 Minuten
Permutations and Combinations•18 Minuten
Circular Permutations•10 Minuten
Combinations•19 Minuten
Factorials and Identity•18 Minuten
Distributing Indistinguishable Items•8 Minuten
R Tutorial•13 Minuten
2 Lektüren•Insgesamt 90 Minuten
Reading References•45 Minuten
Reading References•45 Minuten
3 Aufgaben•Insgesamt 90 Minuten
Combinatorial Analysis•60 Minuten
Fundamentals of Counting in Data Science•15 Minuten
Mastering Combinatorial Techniques: From Combinations to R Applications•15 Minuten
1 Unbewertetes Labor•Insgesamt 60 Minuten
Practice Lab: Exploring Combinatorics and Permutations Using R•60 Minuten
Probability
Modul 3•8 Stunden abzuschließen
Moduldetails
This module introduces the concept of the probability of an event and then shows how probabilities can be computed in certain situations.
Das ist alles enthalten
9 Videos3 Lektüren4 Aufgaben1 Unbewertetes Labor
Infos zu Modulinhalt anzeigen
9 Videos•Insgesamt 141 Minuten
Sample Spaces•14 Minuten
Events•12 Minuten
Venn Diagram•10 Minuten
DeMorgan Laws•11 Minuten
Axioms of Probability•16 Minuten
Simple Propositions•22 Minuten
Equally Likely Outcomes•15 Minuten
ELO Example•13 Minuten
R Tutorial•29 Minuten
3 Lektüren•Insgesamt 180 Minuten
Reading References•60 Minuten
Reading References•60 Minuten
Reading References•60 Minuten
4 Aufgaben•Insgesamt 105 Minuten
Probability•60 Minuten
Understanding Probability: Sample Spaces, Events, and Venn Diagrams•15 Minuten
Foundations of Probability: DeMorgan's Laws and Axioms•15 Minuten
Exploring Probability: Simple Propositions, Equally Likely Outcomes, and R Tutorial•15 Minuten
1 Unbewertetes Labor•Insgesamt 60 Minuten
Practice Lab: Understanding Probability and Combinatorics Using R•60 Minuten
Conditional Probability and Independence
Modul 4•10 Stunden abzuschließen
Moduldetails
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.
Das ist alles enthalten
8 Videos3 Lektüren4 Aufgaben1 Unbewertetes Labor
Infos zu Modulinhalt anzeigen
8 Videos•Insgesamt 73 Minuten
Conditional Probability•10 Minuten
Example Cond Prob•14 Minuten
Reb Balls from Urn•5 Minuten
Revisit Bayes Rule•11 Minuten
Independence•7 Minuten
Ex Medical Testing•12 Minuten
Paradox of the Carnival Dice•9 Minuten
Paradox of the Discrimination Lawsuit•6 Minuten
3 Lektüren•Insgesamt 360 Minuten
Reading References•120 Minuten
Reading References•120 Minuten
Reading References•120 Minuten
4 Aufgaben•Insgesamt 105 Minuten
Conditional Probability and Independence•60 Minuten
Conditional Probability and Practical Examples•15 Minuten
Bayes' Rule and Probability Independence•15 Minuten
Exploring Probability Paradoxes and Real-World Applications•15 Minuten
1 Unbewertetes Labor•Insgesamt 60 Minuten
Practice Lab: COVID-19 Probability Models and Testing Scenarios in R •60 Minuten
Discrete Random Variables
Modul 5•14 Stunden abzuschließen
Moduldetails
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.
Das ist alles enthalten
9 Videos4 Lektüren5 Aufgaben1 Unbewertetes Labor
Infos zu Modulinhalt anzeigen
9 Videos•Insgesamt 176 Minuten
Random Variables•16 Minuten
R.V. Coin Toss•15 Minuten
Coin Toss Proof•9 Minuten
Expected Value•19 Minuten
Expectation of R.V. Function•15 Minuten
Variance of R.V.•13 Minuten
Bernoulli R.V. and Mass Functions•43 Minuten
Defective Product Example•19 Minuten
R Tutorial•28 Minuten
4 Lektüren•Insgesamt 480 Minuten
Reading References•120 Minuten
Reading References•120 Minuten
Reading References•120 Minuten
Reading References•120 Minuten
5 Aufgaben•Insgesamt 120 Minuten
Discrete Random Variables•60 Minuten
Introduction to Random Variables and Coin Tosses•15 Minuten
Understanding Expected Value and Random Variables•15 Minuten
Variance and Bernoulli Random Variables•15 Minuten
Analyzing Defective Products and R Tutorial•15 Minuten
1 Unbewertetes Labor•Insgesamt 60 Minuten
Practice Lab: Statistical Computation and Simulation Using R•60 Minuten
Continuous Random Variables
Modul 6•11 Stunden abzuschließen
Moduldetails
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.
Das ist alles enthalten
10 Videos4 Lektüren5 Aufgaben1 Unbewertetes Labor
Infos zu Modulinhalt anzeigen
10 Videos•Insgesamt 118 Minuten
Continuous RV•10 Minuten
PDF and CDF•13 Minuten
PDF and CDF Example•5 Minuten
Means and Expectation•8 Minuten
Uniform PDF Example•11 Minuten
Cumulative Distribution Function (CDF)•11 Minuten
The Normal Distribution•17 Minuten
Normal Distribution Example•8 Minuten
Other Distributions and the Hazard Rate•20 Minuten
R Tutorial•17 Minuten
4 Lektüren•Insgesamt 360 Minuten
Reading References•90 Minuten
Reading References•90 Minuten
Reading References•90 Minuten
Reading References•90 Minuten
5 Aufgaben•Insgesamt 120 Minuten
Continuous Random Variables•60 Minuten
Continuous Random Variables: PDF and CDF Basics•15 Minuten
Means, Expectation, and Uniform PDF Example•15 Minuten
Understanding CDF and the Normal Distribution•15 Minuten
Exploring Distributions, Hazard Rates, and R•15 Minuten
1 Unbewertetes Labor•Insgesamt 60 Minuten
Practice Lab: Statistical Simulations and Probability Modeling in R•60 Minuten
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