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Unformatted text preview: ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Solution to Homework 5 October 19, 2011 1. Solution: ( 1 3 n ) n 1 = ( 1 3 n ) n * ( 1 3 n ) ( 1 ) , the first part converges to e 3 and the 2nd part converges to 1, so lim n ( 1 3 n ) n 1 = e 3 . 2. Solution: (a)Bernoulli. (b)Geometric. (c)Binomial. (d)Bernoulli. (e)Geometric. (f)None of the three. 3. Solution: (a) Pr { Y = k } = 1 3 , k = 1 2 , k = 1 1 6 , k = 2 (b)E [ Y ] = 1 3 + 1 2 1 + 1 6 2 = 1 2 + 1 3 = 5 6 . (c)E [ Y 2 ] = 1 3 2 + 1 2 1 2 + 1 6 2 2 = 1 2 + 2 3 = 7 6 . (d) Var ( Y ) = E [ Y 2 ]  ( E [ Y ]) 2 = 7 6 25 36 = 17 36 . (e) p Var ( Y ) = 17 6 . (f) c < E [ Y ] , so c can be 5 6 , you would still be willing play. 4. Solution: (a) ( 50 20 ) ( 100 40 ) . (b)1 ( 50 40 )( 2 1 ) 40 ( 100 40 ) . (c) ( 50 k )( 2 2 ) k ( 50 k 40 2 k )( 2 1 ) 40 2 k ( 100 40 ) . 5. Solution: (a) = E [ X ] = 1 3 9 10 + 7 1 10 = 1....
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This note was uploaded on 01/22/2012 for the course ISYE 2027 taught by Professor Zahrn during the Fall '08 term at Georgia Institute of Technology.
 Fall '08
 Zahrn

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