b.lect10 - Outline Some Common Discrete Distributions...

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Unformatted text preview: Outline Some Common Discrete Distributions Lecture 10 Chapter 3: Random Variables and Their Distributions Michael Akritas Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable I A r.v. X is called Bernoulli if it takes only two values. Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable I A r.v. X is called Bernoulli if it takes only two values. I The two values are referred to as success (S) and failure (F), or are re-coded as 1 and 0. Thus, always, S X = { , 1 } . Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable I A r.v. X is called Bernoulli if it takes only two values. I The two values are referred to as success (S) and failure (F), or are re-coded as 1 and 0. Thus, always, S X = { , 1 } . I Experiments resulting in a Bernoulli r.v. are called Bernoulli . Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable I A r.v. X is called Bernoulli if it takes only two values. I The two values are referred to as success (S) and failure (F), or are re-coded as 1 and 0. Thus, always, S X = { , 1 } . I Experiments resulting in a Bernoulli r.v. are called Bernoulli . Example 1. A product is inspected. Set X = 1 if defective, X = 0 if non-defective. Michael Akritas Lecture 10 Chapter 3: Random Variables and Their Distribution Outline Some Common Discrete Distributions The Bernoulli Random Variable The Binomial Random Variable The Hypergeometric Random Variable The Negative Binomial Random Variable I A r.v. X is called Bernoulli if it takes only two values....
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b.lect10 - Outline Some Common Discrete Distributions...

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