Probability: Continuous Random Variables

Course Description

Welcome to our advanced statistics and data analysis course, "Probability: Continuous Random Variables," offered by PurdueX! This intermediate-level course is designed to deepen your understanding of probability concepts and their applications in data science. Building upon the foundation of discrete random variables, this course takes you into the fascinating world of continuous random variables and their probability distributions.

What students will learn from the course:

• In-depth knowledge of continuous random variables and their properties
• Understanding of key probability distribution models, including exponential, Gamma, Beta, and normal distributions
• Application of the Central Limit Theorem (CLT) to connect various distributions with the Normal distribution
• Advanced probability topics such as Markov and Chebyshev inequalities, order statistics, moment generating functions, and transformation of random variables
• Practical skills in applying these concepts to real-world data analysis and information science problems

Pre-requisites or skills necessary to complete the course:

• Basic Calculus 1 & 2, and Calculus 3 (including an understanding of double integrals)
• Completion of the course "416.1x Probability: Basic Concepts & Discrete Random Variables"
• Familiarity with basic probability concepts and discrete random variables

What the course will cover:

• Continuous random variables and their properties
• Joint density/CDF and properties of independent continuous random variables
• Conditional distributions for continuous random variables
• Expected values of continuous random variables and functions of random variables
• Probability distribution models: Uniform, Exponential, Gamma, and Beta distributions
• Normal distribution and Central Limit Theorem (CLT)
• Applications of CLT to approximate various distribution models
• Covariance and conditional expectation
• Markov and Chebyshev inequalities
• Order statistics
• Moment generating functions
• Transformation of random variables

Who this course is for:

This course is ideal for:

• Data science and analytics professionals looking to enhance their statistical knowledge
• Computer science students interested in information science and machine learning
• Engineers and researchers working with large datasets and complex systems
• Anyone seeking to advance their career in fields related to data analysis and information processing

How learners can use these skills in the real world:

The skills acquired in this course are invaluable for:

• Analyzing and interpreting complex datasets in various industries
• Developing predictive models and algorithms for machine learning applications
• Improving decision-making processes based on statistical analysis
• Enhancing research methodologies in fields such as finance, healthcare, and social sciences
• Optimizing processes and systems using probability-based approaches
• Contributing to cutting-edge developments in information science and data-driven technologies

Syllabus:

By enrolling in this course, you'll be taking a significant step towards mastering the intricacies of probability and statistics, setting yourself up for success in the ever-growing field of data science and information analysis. Join us on this exciting journey to unlock the power of continuous random variables and their applications in the real world!