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

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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 ”....
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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.

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

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