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Data Science

155Definition and Properties of Continuous Random Variables
156Probability Density Functions (PDFs)
157Cumulative Distribution Functions (CDFs) for Continuous Variables
158Computing Probabilities Using Integration
159Expected Value and Variance for Continuous Variables
160Percentiles and Quantiles from CDFs
161The Continuous Uniform Distribution
162Uniform Distribution: PDF and CDF
163Uniform Distribution: Mean and Variance
164The Exponential Distribution
165Exponential Distribution: PDF and CDF
166Exponential Distribution: Mean and Variance
167Memoryless Property of Exponential
168Applications: Uniform and Exponential in Practice
169The Normal Distribution: Definition and Properties
170Parameters: Mean (μ) and Standard Deviation (σ)
171The 68-95-99.7 Rule (Empirical Rule)
172Probability Density Function for Normal Distribution
173Calculating Probabilities with the Normal Distribution
174Symmetry and the Mode, Median, Mean
175Linear Transformations of Normal Variables
176Sum of Independent Normal Variables
177Real-World Applications of the Normal Distribution
178Log-Normal Distribution: Definition and Properties
179When Variables Are Log-Normally Distributed
180Parameters and Moments of the Log-Normal
181Gamma Distribution: Shape and Rate Parameters
182Special Cases: Exponential and Chi-Squared
183Applications of the Gamma Distribution
184Beta Distribution: Bounded Between 0 and 1
185Beta Distribution Shapes and Flexibility
186Using Beta for Proportions and Probabilities
187The Weibull Distribution: Shape, Scale, and Survival
188Weibull Distribution: Hazard Function and Reliability
189Fitting Weibull Models to Lifetime Data
190The Pareto Distribution: Heavy Tails and Power Laws
191Pareto Principle and the 80/20 Rule
192Applications: Income, Wealth, and Network Effects
193Choosing Between Distributions in Practice

Data Science

155Definition and Properties of Continuous Random Variables
156Probability Density Functions (PDFs)
157Cumulative Distribution Functions (CDFs) for Continuous Variables
158Computing Probabilities Using Integration
159Expected Value and Variance for Continuous Variables
160Percentiles and Quantiles from CDFs
161The Continuous Uniform Distribution
162Uniform Distribution: PDF and CDF
163Uniform Distribution: Mean and Variance
164The Exponential Distribution
165Exponential Distribution: PDF and CDF
166Exponential Distribution: Mean and Variance
167Memoryless Property of Exponential
168Applications: Uniform and Exponential in Practice
169The Normal Distribution: Definition and Properties
170Parameters: Mean (μ) and Standard Deviation (σ)
171The 68-95-99.7 Rule (Empirical Rule)
172Probability Density Function for Normal Distribution
173Calculating Probabilities with the Normal Distribution
174Symmetry and the Mode, Median, Mean
175Linear Transformations of Normal Variables
176Sum of Independent Normal Variables
177Real-World Applications of the Normal Distribution
178Log-Normal Distribution: Definition and Properties
179When Variables Are Log-Normally Distributed
180Parameters and Moments of the Log-Normal
181Gamma Distribution: Shape and Rate Parameters
182Special Cases: Exponential and Chi-Squared
183Applications of the Gamma Distribution
184Beta Distribution: Bounded Between 0 and 1
185Beta Distribution Shapes and Flexibility
186Using Beta for Proportions and Probabilities
187The Weibull Distribution: Shape, Scale, and Survival
188Weibull Distribution: Hazard Function and Reliability
189Fitting Weibull Models to Lifetime Data
190The Pareto Distribution: Heavy Tails and Power Laws
191Pareto Principle and the 80/20 Rule
192Applications: Income, Wealth, and Network Effects
193Choosing Between Distributions in Practice

← Data Science

Lesson 171 of 2,145·5. Continuous Probability DistributionsPro lesson

The 68-95-99.7 Rule (Empirical Rule)

Master the fundamental rule that ~68% of data falls within 1σ, ~95% within 2σ, and ~99.7% within 3σ.

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