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# hw6solns - Solutions to Homework 6 4.78 Let Y be the number...

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Solutions to Homework 6 4.78 Let Y be the number of people who refuse to be interviewed before she obtains five people, so 5, Y X = - Y can reasonably be assumed to have the negative binomial distribution with 0.6 p = , 5 r = a. ( 29 ( 29 2 5 0 ( 7) ( 2) 4 0.6 1 0.6 4 0.419904 i i P X P Y i = = + = - = b. 2 2 5 0.4 10 5 0.4 50 ( ) , ( ) 0.6 3 0.6 9 rq rq E Y V Y p p × × = = = = = = Because 5, Y X = - so 5 X Y = + , then 25 50 ( ) ( ) 5 , ( ) ( ) 3 9 E X E Y V X V Y = + = = = 4.79 Let X be the number of customers that the salesman has to visit to make three sales, let Y denote the number of customers who refuse to purchase a car before the salesman makes three sales, so 3 Y X = - . Suppose that trials are independent, Y can be modeled as negative binomial distribution with 0.2, 3 p r = = a. ( 29 ( 29 1 3 0 ( 5) ( 2) 1 ( 1) 2 1 0.2 1 0.2 2 0.9728 i i P X P Y P Y i = = = - + = - - = b. 3 0.8 ( ) 12 0.2 rq E Y p × = = = Because 3, Y X = - so 3 X Y = + , then

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( ) ( ) 3 15 E X E Y = + = 4.83 a. Let i Y denote the event that John wins in the i th game, ( 1) 0.6 i P Y p = = = . Because the outcome of each game is independent of the outcomes of the other games, then 3 1 2 3 ( 3) (
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hw6solns - Solutions to Homework 6 4.78 Let Y be the number...

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