solution4 - EL630: Homework4 Solutions 1) {First 2 appears...

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Unformatted text preview: EL630: Homework4 Solutions 1) {First 2 appears at n th roll} = } 2 , 2 , . . . . , 2 , 2 , 2 { . That is, we get 1- n rolls in which 2 does not appear, and then the 2 appears on the n th roll. Since the rolls are independent, the probability of this happening is =- 6 1 6 5 } 2 { 1 n th roll n at appears First P . Thus, = =- 6 1 6 5 ) ( 1 n n X P . Therefore, = + < < = = =- ... , 3 , 2 , 1 ; 1 6 1 6 5 1 ) ( ) ( 1 1 m m x m x x X P x F m n n X 2) This problem looks like an application of the Demoivre-Laplace theorem with 5000 = n , 2 / 1 = p , 2 / 1 = q , except that the lower limit of 2,225 is not within the range of the theorems assumptions. That is, 35 ) 2 / 1 )( 2 / 1 )( 5000 ( = = npq in this case, but the lower limit is more than 35 away from the np point of 2,500. But we can use Bernoulis theorem from the end of lecture 2 here. we can use Bernoulis theorem from the end of lecture 2 here....
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solution4 - EL630: Homework4 Solutions 1) {First 2 appears...

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