Lecture9 - lecture 9, Discrete Random Variables II 1/25 The...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lecture 9, Discrete Random Variables II 1/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II Outline 1 The Bernoulli Distribution 2 The Binomial Distribution Examples lecture 9, Discrete Random Variables II 2/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II The Bernoulli Distribution The Bernoulli Distribution A Bernoulli trial is an experiment with two outcomes: “success” and “failure” • Let p be the probability of success — The probability of failure, q , is 1- p • put X = ( 1 , if succeeds, , otherwise • X is called a Bernoulli ( p ) random variable lecture 9, Discrete Random Variables II 3/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II The Bernoulli Distribution Examples of Bernoulli Trials 1 Will the coin land heads? 2 Will the newborn child be a girl? 3 Will a potential customer buy a product? 4 Will a voter vote for a specific candidate? lecture 9, Discrete Random Variables II 4/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II The Bernoulli Distribution Mean and Variance of Bernoulli Random Variables • Let X be a Bernoulli ( p ) random variable. X has probability distribution x 1 p ( x ) p q , where q = 1- p . • Hence μ = E ( X ) = σ 2 = Var ( X ) = σ = SD ( X ) = . lecture 9, Discrete Random Variables II 5/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II The Binomial Distribution The Binomial Distribution A binomial experiment is an experiment satisfying the following conditions: 1 Experiment consists of a fixed number (say, n ) of trials 2 Each trial is a Bernoulli trial 3 Probability of success, p , is constant from trial to trial — The probability of failure, q , is 1- p 4 Trials are independent • Let S be the total number of successes in the n trials, then S is said to be a binomial ( n , p ) random variable • Possible values that S can take are 0 , 1 ,..., n . • Let X i =1 if the i th trial succeeds, and = 0 otherwise. Then X i is a Bernoulli(p) random variable, and S = X 1 + ... + X n . lecture 9, Discrete Random Variables II 6/25 The Bernoulli Distribution The Binomial Distribution Examples lecture 9, Discrete Random Variables II The Binomial Distribution Examples Examples of Binomial Random Variable 1 Number of 1’s in 10 rolls of a die is a random variable. 2 A multiple-choice test contains 25 questions, each has four choices and one correct answer. The number of correct guesses on the test is a random variable. Binomial or not: 3 A couple decides to have children until they have a girl....
View Full Document

This note was uploaded on 12/28/2010 for the course BUSINESS A ISOM 111 taught by Professor Yingyingli during the Fall '10 term at HKUST.

Page1 / 25

Lecture9 - lecture 9, Discrete Random Variables II 1/25 The...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online