Steve Brunton

Confidence Intervals
Confidence Intervals
Normal Approximation to Sample Mean
Normal Approximation to Sample Mean
Sample Variance in Random Population Sampling
Sample Variance in Random Population Sampling
Random Sampling Without Replacement (Finite
Random Sampling Without Replacement (Finite "n" Correction)
Random Sampling in Statistics: Expected Value and Variance of the Sample Mean
Random Sampling in Statistics: Expected Value and Variance of the Sample Mean
Population Statistics and Random Sampling
Population Statistics and Random Sampling
Introduction to Statistics and Data Analysis
Introduction to Statistics and Data Analysis
Proof of the Central Limit Theorem
Proof of the Central Limit Theorem
The Tail Sum Formula in Probability
The Tail Sum Formula in Probability
Covariance and Correlation: Example with Gaussian Distributions
Covariance and Correlation: Example with Gaussian Distributions
Covariance and Correlation in Probability
Covariance and Correlation in Probability
The Lebesque Measure in Probability
The Lebesque Measure in Probability
Additive Property of the Moment Generating Function
Additive Property of the Moment Generating Function
Example of The Moment Generating Function
Example of The Moment Generating Function
The Moment Generating Function
The Moment Generating Function
The Central Limit Theorem
The Central Limit Theorem
The Law of Large Numbers
The Law of Large Numbers
Chebyshev's Inequality in Probability: Second Order Estimates
Chebyshev's Inequality in Probability: Second Order Estimates
Markov's Inequality in Probability: First Order Estimates
Markov's Inequality in Probability: First Order Estimates
Two Examples of Expected Values & Functions: Temperature in C vs F, and the Kinetic Theory of Gases
Two Examples of Expected Values & Functions: Temperature in C vs F, and the Kinetic Theory of Gases
Example of Computing the Expectation and Variance of an Exponential Distribution
Example of Computing the Expectation and Variance of an Exponential Distribution
Properties of the Expected Value
Properties of the Expected Value
Variance and Standard Deviation
Variance and Standard Deviation
The Expected Value (Mean) of a Probability Distribution
The Expected Value (Mean) of a Probability Distribution
Joint Probability Distributions: Marginal and Conditional Densities
Joint Probability Distributions: Marginal and Conditional Densities
Joint Probability Distributions
Joint Probability Distributions
The Chi Squared Distribution: The Square of the Normal Distribution
The Chi Squared Distribution: The Square of the Normal Distribution
Rescaling the Normal Distribution to Mean Zero and Variance One
Rescaling the Normal Distribution to Mean Zero and Variance One
Functions of a Random Variable
Functions of a Random Variable
The Gamma Distribution
The Gamma Distribution