Explore the concept of random variables in this comprehensive video series. Delve into continuous random variables, probability density functions, and their conditions. Learn to evaluate probabilities, handle unknowns, and work with domain restrictions. Master integration skills for bounded and unbounded integrals, and understand uniform distributions. Discover how to find the mode, median, and percentiles of continuous probability distributions. Examine expected values and variance, including proofs and worked examples. Study cumulative distribution functions and their applications. Investigate the normal distribution, its probability density function, and how to analyze normally distributed empirical data. Apply the trapezoidal rule to normal distributions and learn to integrate them using technology. Interpret statistical tables and explore variance on modified distributions through worked examples and investigations.
Overview
Syllabus
What are Continuous Random Variables? (1 of 3: Relation to discrete data).
What are Continuous Random Variables? (2 of 3: Why we need different tools).
What are Continuous Random Variables? (3 of 3: Conditions for a Probability Density Function).
Probability Density Functions (1 of 7: Meeting the conditions).
Probability Density Functions (2 of 7: Evaluating a probability).
Probability Density Functions (3 of 7: Unknowns in the function).
Probability Density Functions (4 of 7: Domain restrictions).
Probability Density Functions (5 of 7: Reviewing integration skills).
Probability Density Functions (6 of 7: Unbounded integrals).
Probability Density Functions (7 of 7: Uniform distributions).
Mode & Median of a Continuous Probability Distribution.
Locating Boundaries of a Distribution from its Median.
Finding Percentiles of a Continuous Probability Distribution.
Expected Value of a Continuous Distribution (1 of 2: Relation to discrete data).
Expected Value of a Continuous Distribution (2 of 2: Worked example).
Probability Density Functions Q&A (1 of 2: Evaluating probabilities).
Probability Density Functions Q&A (2 of 2: Two approaches to an unbounded probability).
Variance (1 of 4: Introducing the formulas).
Variance (2 of 4: Worked example with first formula).
Variance (3 of 4: Worked example with second formula).
Variance (4 of 4: Proof of two formulas).
Cumulative Distribution Function (2 of 3: Evaluating probabilities).
Cumulative Distribution Function (1 of 3: Definition).
Cumulative Distribution Function (3 of 3: Locating quantiles).
Probability Density Functions Q&A (1 of 2: Evaluating probabilities).
Probability Density Functions Q&A (2 of 2: Two approaches to an unbounded probability).
What is the Normal Distribution?.
Normally Distributed Empirical Data (1 of 2: Comparing marathon times).
Normally Distributed Empirical Data (2 of 2: Calculating population proportions).
Probability Density Function of the Normal Distribution.
Trapezoidal Rule on Normal Distribution (1 of 2: Reviewing the formula).
Trapezoidal Rule on Normal Distribution (2 of 2: Verifying empirical result).
Integrating Normal Distribution with Technology (1 of 2: One-sided inequality).
Integrating Normal Distribution with Technology (2 of 2: Contrasting populations).
Statistical Tables (1 of 2: How to interpret values).
Statistical Tables (2 of 2: Combining results).
Variance on a Modified Distribution (1 of 2: Worked example).
Variance on a Modified Distribution (2 of 2: Investigating the modifications).
Taught by
Eddie Woo
