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Variance (4 of 4: Proof of two formulas)
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Classroom Contents
Random Variables
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- 1 What are Continuous Random Variables? (1 of 3: Relation to discrete data)
- 2 What are Continuous Random Variables? (2 of 3: Why we need different tools)
- 3 What are Continuous Random Variables? (3 of 3: Conditions for a Probability Density Function)
- 4 Probability Density Functions (1 of 7: Meeting the conditions)
- 5 Probability Density Functions (2 of 7: Evaluating a probability)
- 6 Probability Density Functions (3 of 7: Unknowns in the function)
- 7 Probability Density Functions (4 of 7: Domain restrictions)
- 8 Probability Density Functions (5 of 7: Reviewing integration skills)
- 9 Probability Density Functions (6 of 7: Unbounded integrals)
- 10 Probability Density Functions (7 of 7: Uniform distributions)
- 11 Mode & Median of a Continuous Probability Distribution
- 12 Locating Boundaries of a Distribution from its Median
- 13 Finding Percentiles of a Continuous Probability Distribution
- 14 Expected Value of a Continuous Distribution (1 of 2: Relation to discrete data)
- 15 Expected Value of a Continuous Distribution (2 of 2: Worked example)
- 16 Probability Density Functions Q&A (1 of 2: Evaluating probabilities)
- 17 Probability Density Functions Q&A (2 of 2: Two approaches to an unbounded probability)
- 18 Variance (1 of 4: Introducing the formulas)
- 19 Variance (2 of 4: Worked example with first formula)
- 20 Variance (3 of 4: Worked example with second formula)
- 21 Variance (4 of 4: Proof of two formulas)
- 22 Cumulative Distribution Function (2 of 3: Evaluating probabilities)
- 23 Cumulative Distribution Function (1 of 3: Definition)
- 24 Cumulative Distribution Function (3 of 3: Locating quantiles)
- 25 Probability Density Functions Q&A (1 of 2: Evaluating probabilities)
- 26 Probability Density Functions Q&A (2 of 2: Two approaches to an unbounded probability)
- 27 What is the Normal Distribution?
- 28 Normally Distributed Empirical Data (1 of 2: Comparing marathon times)
- 29 Normally Distributed Empirical Data (2 of 2: Calculating population proportions)
- 30 Probability Density Function of the Normal Distribution
- 31 Trapezoidal Rule on Normal Distribution (1 of 2: Reviewing the formula)
- 32 Trapezoidal Rule on Normal Distribution (2 of 2: Verifying empirical result)
- 33 Integrating Normal Distribution with Technology (1 of 2: One-sided inequality)
- 34 Integrating Normal Distribution with Technology (2 of 2: Contrasting populations)
- 35 Statistical Tables (1 of 2: How to interpret values)
- 36 Statistical Tables (2 of 2: Combining results)
- 37 Variance on a Modified Distribution (1 of 2: Worked example)
- 38 Variance on a Modified Distribution (2 of 2: Investigating the modifications)
