Principles of Probability and Random Variables

What you'll learn
Core principles of probability, including events, outcomes, and rules
Discrete and continuous random variables, and how to work with them
Probability mass functions (PMF), density functions (PDF), and cumulative distribution functions (CDF)
Expected value, variance, and functions of random variables
The normal distribution and its applications
Joint, marginal, and conditional distributions for multiple random variables
Covariance, correlation, and independence
Conditional expectation and variance
Requirements
Basic algebra and mathematical reasoning
No prior knowledge of probability or statistics required
Description
Unlock the power of probability and random variables with this comprehensive course designed for students, professionals, and lifelong learners. Whether you're preparing for exams, diving into data science, or strengthening your statistical foundation, this course offers a clear, structured, and intuitive journey through the core concepts of probability theory and random variables.This course breaks down complex topics into digestible lessons, using real-world examples and visual explanations to help you build a deep and lasting understanding.Course StructureThe course is divided into 10 comprehensive chapters:Fundamentals of ProbabilityUnderstand the building blocks of probability including events, outcomes, and rules.Random VariablesLearn what random variables are and how they relate to probability.Discrete Random VariablesDive into PMFs, CDFs, and expected values for discrete variables.Continuous Random VariablesExplore PDFs, CDFs, and expected values for continuous variables.Variance and Functions of Random VariablesAnalyze how functions affect random variables and how to compute variance.The Normal DistributionMaster the standard and general normal distributions.Multiple Random VariablesLearn about joint, marginal, and conditional distributions.Functions of Several Random VariablesUnderstand how to handle and analyze multiple random variables together.Covariance and CorrelationMeasure relationships between variables and understand their dependencies.Conditional Expectation and VarianceExplore advanced concepts in conditional analysis.Course Features39 high-quality video lecturesClear explanations with visual aidsLifetime access and downloadable resourcesCertificate of completionLearn at your own pace
Who this course is for
University students studying statistics, mathematics, or engineering
Data analysts and data scientists seeking a solid foundation in probability
Professionals preparing for exams like GRE, GMAT, CFA, or actuarial tests
Anyone curious about how randomness and uncertainty are modeled mathematically
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