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Chebyshev's Inequality in Probability: Second Order Estimates
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Classroom Contents
Probability Bootcamp
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- 1 Probability and Statistics: Overview
- 2 Gentle Introduction to Probability: Counting Coin Flips and Dice
- 3 Counting Probabilities with Combinatorics and the Factorial
- 4 Set Theory in Probability: Sample Spaces and Events
- 5 The Birthday Problem in Probability: P(A) = 1 - P(not A)
- 6 Quality Control, Non-Destructive Inspection, and the Multinomial Distribution
- 7 The Binomial Distribution and the Multinomial Distribution
- 8 Conditional Probabilities
- 9 The Law of Total Probability
- 10 Bayes' Theorem (with Example!)
- 11 Bayes' Theorem Example: Drug Testing 🌿
- 12 Independence in Probability
- 13 Random Variables and Probability Distributions
- 14 Bernoulli and Binomial Random Variables
- 15 The Normal Distribution: The Limit of Binomial Distribution for Large "n"
- 16 The Standard Unit Normal and Probability Computations
- 17 The Poisson Distribution: The Rare Event Limit of a Binomial Distribution
- 18 The Geometric Distribution: The First Success of a Bernoulli Distribution
- 19 The Exponential Distribution: Time Between Poisson Events
- 20 The Hazard Rate and Memoryless Property of the Exponential Distribution
- 21 The Connection Between the Exponential Distribution and the Poisson Process
- 22 The Gamma Distribution
- 23 Functions of a Random Variable
- 24 Rescaling the Normal Distribution to Mean Zero and Variance One
- 25 The Chi Squared Distribution: The Square of the Normal Distribution
- 26 Joint Probability Distributions
- 27 Joint Probability Distributions: Marginal and Conditional Densities
- 28 The Expected Value (Mean) of a Probability Distribution
- 29 Properties of the Expected Value
- 30 Variance and Standard Deviation
- 31 Example of Computing the Expectation and Variance of an Exponential Distribution
- 32 Two Examples of Expected Values & Functions: Temperature in C vs F, and the Kinetic Theory of Gases
- 33 Markov's Inequality in Probability: First Order Estimates
- 34 Chebyshev's Inequality in Probability: Second Order Estimates
- 35 The Law of Large Numbers
- 36 The Central Limit Theorem
- 37 The Moment Generating Function
- 38 Example of The Moment Generating Function
- 39 The Lebesque Measure in Probability
- 40 Additive Property of the Moment Generating Function
- 41 Covariance and Correlation in Probability
- 42 Covariance and Correlation: Example with Gaussian Distributions
- 43 The Tail Sum Formula in Probability
- 44 Proof of the Central Limit Theorem
