sta4321-10

# sta4321-10 - Bernoulli and Binomial Distributions Bernoulli...

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

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Bernoulli and Binomial Distributions Bernoulli Distribution Binomial Distribution Exercises Bernoulli Distribution a flipped coin turns up either heads or tails an item on an assembly line is either defective or not defective a piece of fruit is either damaged or not damaged a cow is either pregnant or not pregnant a child is either female or male X = 1 , if the outcome of the trial is a success , if the outcome of the trial is a failure X = 1 , w.p. p , w.p. q = 1- p We can write the pmf as p ( x ) = p x ( 1- p ) 1- x , x = , 1 Arthur Berg Bernoulli and Binomial Distributions 2/ 9 Bernoulli Distribution Binomial Distribution Exercises Bernoulli Distribution a flipped coin turns up either heads or tails an item on an assembly line is either defective or not defective a piece of fruit is either damaged or not damaged a cow is either pregnant or not pregnant a child is either female or male X = 1 , if the outcome of the trial is a success , if the outcome of the trial is a failure X = 1 , w.p. p , w.p. q = 1- p We can write the pmf as p ( x ) = p x ( 1- p ) 1- x , x = , 1 Arthur Berg Bernoulli and Binomial Distributions 2/ 9 Bernoulli Distribution Binomial Distribution Exercises Bernoulli Distribution a flipped coin turns up either heads or tails an item on an assembly line is either defective or not defective a piece of fruit is either damaged or not damaged a cow is either pregnant or not pregnant a child is either female or male X = 1 , if the outcome of the trial is a success , if the outcome of the trial is a failure X = 1 , w.p. p , w.p. q = 1- p We can write the pmf as p ( x ) = p x ( 1- p ) 1- x , x = , 1 Arthur Berg Bernoulli and Binomial Distributions 2/ 9 Bernoulli Distribution Binomial Distribution Exercises Bernoulli Distribution a flipped coin turns up either heads or tails an item on an assembly line is either defective or not defective a piece of fruit is either damaged or not damaged a cow is either pregnant or not pregnant a child is either female or male X = 1 , if the outcome of the trial is a success , if the outcome of the trial is a failure X = 1 , w.p. p , w.p. q = 1- p We can write the pmf as p ( x ) = p x ( 1- p ) 1- x , x = , 1 Arthur Berg Bernoulli and Binomial Distributions 2/ 9 Bernoulli Distribution Binomial Distribution Exercises Expectation and Variance of Bernoulli( p ) E ( X ) = 1 x = xp ( x ) = p ( ) + 1 p ( 1 ) = ( 1- p ) + 1 ( p ) = p Noting that when X ∼ Bernoulli ( p ) , X 2 ∼ X , i.e. “ X 2 has the same distribution as X ”....
View Full Document

## This note was uploaded on 10/04/2011 for the course STA 4321 taught by Professor Staff during the Fall '08 term at University of Florida.

### Page1 / 24

sta4321-10 - Bernoulli and Binomial Distributions Bernoulli...

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

View Full Document
Ask a homework question - tutors are online