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Foundations of Probability and Random Variables · LearnSpace
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Foundations of Probability and Random Variables

Курс от Johns Hopkins University
Средний≈ 49.1 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

Probability DistributionProbabilityBayesian StatisticsCombinatoricsProbability & StatisticsR ProgrammingData ScienceStatistical AnalysisSimulationsStatisticsData AnalysisStatistical MethodsStatistical ProgrammingApplied Machine Learning

Программа курса

6 модулей · 90 учебных материалов

01Course Introduction3 материалов
Course OverviewЧтениеInstructor Biography - Dr. Ian McCullohPLUGINInstructor Biography - Dr. Tony JohnsonЧтение
02Combinatorial Analysis15 материалов

Fundamentals of Counting in Data Science

Учитесь у экспертов

Ian McCulloh

Преподаватель курса

Tony Johnson

Преподаватель курса

Foundations of Probability and Random Variables
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Обучение на Coursera

≈ 49.1 ч

6 модулей

Язык: Английский

Субтитры: Узбекский, Испанский, Казахский, Венгерский

Часть программы вашего университета
Introduction to Data ScienceВидео
Basic Principle of CountingВидео
Generalized Principle of CountingВидео
Permutations and CombinationsВидео
Circular PermutationsВидео
Reading ReferencesЧтение
Fundamentals of Counting in Data ScienceЗадание

Mastering Combinatorial Techniques: From Combinations to R Applications

CombinationsВидеоFactorials and IdentityВидеоDistributing Indistinguishable ItemsВидеоR TutorialВидеоReading ReferencesЧтениеMastering Combinatorial Techniques: From Combinations to R ApplicationsЗадание

Module-end Assessments

Practice Lab: Exploring Combinatorics and Permutations Using RЛабораторнаяCombinatorial AnalysisЗадание
03Probability17 материалов

Understanding Probability: Sample Spaces, Events, and Venn Diagrams

Sample SpacesВидеоEventsВидеоVenn DiagramВидеоReading ReferencesЧтениеUnderstanding Probability: Sample Spaces, Events, and Venn DiagramsЗадание

Foundations of Probability: DeMorgan's Laws and Axioms

DeMorgan LawsВидеоAxioms of ProbabilityВидеоReading ReferencesЧтениеFoundations of Probability: DeMorgan's Laws and AxiomsЗадание

Exploring Probability: Simple Propositions, Equally Likely Outcomes, and R Tutorial

Simple PropositionsВидеоEqually Likely OutcomesВидеоELO ExampleВидеоR TutorialВидеоReading ReferencesЧтениеExploring Probability: Simple Propositions, Equally Likely Outcomes, and R TutorialЗадание

Module-end Assessments

Practice Lab: Understanding Probability and Combinatorics Using RЛабораторнаяProbabilityЗадание
04Conditional Probability and Independence16 материалов

Conditional Probability and Practical Examples

Conditional ProbabilityВидеоExample Cond ProbВидеоReb Balls from UrnВидеоReading ReferencesЧтениеConditional Probability and Practical ExamplesЗадание

Bayes' Rule and Probability Independence

Revisit Bayes RuleВидео IndependenceВидеоReading ReferencesЧтениеBayes' Rule and Probability IndependenceЗадание

Exploring Probability Paradoxes and Real-World Applications

Ex Medical TestingВидеоParadox of the Carnival DiceВидеоParadox of the Discrimination LawsuitВидеоReading ReferencesЧтениеExploring Probability Paradoxes and Real-World ApplicationsЗадание

Module-end Assessments

Practice Lab: COVID-19 Probability Models and Testing Scenarios in R ЛабораторнаяConditional Probability and IndependenceЗадание
05Discrete Random Variables19 материалов

Introduction to Random Variables and Coin Tosses

Random VariablesВидеоR.V. Coin TossВидеоCoin Toss ProofВидеоReading ReferencesЧтениеIntroduction to Random Variables and Coin TossesЗадание

Understanding Expected Value and Random Variables

Expected ValueВидеоExpectation of R.V. FunctionВидеоReading ReferencesЧтениеUnderstanding Expected Value and Random VariablesЗадание

Variance and Bernoulli Random Variables

Variance of R.V.ВидеоBernoulli R.V. and Mass FunctionsВидеоReading ReferencesЧтениеVariance and Bernoulli Random VariablesЗадание

Analyzing Defective Products and R Tutorial

Defective Product ExampleВидео R TutorialВидеоReading ReferencesЧтениеAnalyzing Defective Products and R TutorialЗадание

Module-end Assessments

Practice Lab: Statistical Computation and Simulation Using RЛабораторнаяDiscrete Random VariablesЗадание
06Continuous Random Variables20 материалов

Continuous Random Variables: PDF and CDF Basics

Continuous RVВидеоPDF and CDFВидеоPDF and CDF ExampleВидеоReading ReferencesЧтениеContinuous Random Variables: PDF and CDF BasicsЗадание

Means, Expectation, and Uniform PDF Example

Means and ExpectationВидеоUniform PDF ExampleВидеоReading ReferencesЧтениеMeans, Expectation, and Uniform PDF ExampleЗадание

Understanding CDF and the Normal Distribution

Cumulative Distribution Function (CDF)ВидеоThe Normal DistributionВидеоNormal Distribution ExampleВидеоReading ReferencesЧтениеUnderstanding CDF and the Normal DistributionЗадание

Exploring Distributions, Hazard Rates, and R

Other Distributions and the Hazard RateВидеоR TutorialВидеоReading ReferencesЧтениеExploring Distributions, Hazard Rates, and RЗадание

Module-end Assessments

Practice Lab: Statistical Simulations and Probability Modeling in RЛабораторнаяContinuous Random VariablesЗадание