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hw2 - (a Z i =(13 Z i-1 13 mod 16(b Z i =(12 Z i-1 13 mod...

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AMS 553: Homework 2 1. (L&K 7.1) Consider the LCG Z i = (5 Z i + 3)( mod 16) and Z 0 = 7. Find Z 500 , using only pencil and paper. 2. (L&K 7.2) For the following multiplicative LCGs, compute Z i for enough values of i 1 to cover an entire cycle: (a) Z i = (11 Z i - 1 )( mod 16) , Z 0 = 1 (b) Z i = (11 Z i - 1 )( mod 16) , Z 0 = 2 (c) Z i = (2 Z i - 1 )( mod 13) , Z 0 = 1 (d) Z i = (3 Z i - 1 )( mod 13) , Z 0 = 1 Note that (a) and (b) have m of the form 2 b ; (c) is a PMMLCG, for which a = 2 is a primitive element modulo m = 13. 3. (L&K 7.3) Without actually computing any Z i ’s, determine which of the following mixed LCGs have full period:
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Unformatted text preview: (a) Z i = (13 Z i-1 + 13)( mod 16) (b) Z i = (12 Z i-1 + 13)( mod 16) (c) Z i = (13 Z i-1 + 12)( mod 16) (d) Z i = ( Z i-1 + 12)( mod 13) For part (d), also plot the pairs ( U 1 ,U 2 ) , ( U 2 ,U 3 ) ,... . Are there any obvious undesirable structure? 4. Without generating any Z i ’s, determine which of the following multiplicative LCGs is an PMMLCG? (a) Z i = (2 Z i-1 )( mod 19) (b) Z i = (4 Z i-1 )( mod 15) (c) Z i = (97 Z i-1 )( mod 9021)...
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