# solution01 - while that for = 128 should oscillate around....

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Solutions to Homework 01 1. One possible program: #include <stdio.h> #include <stdlib.h> #include <math.h> main(int argc, char **argv) { int i, alpha, old, new; if (argc != 3) { printf("Too few arguments \n"); printf("Usage: %s <alpha> <X_0> ", argv[0]); exit(1); } alpha = atoi(argv[2]); old = atoi(argv[3]); for (i=0; i<1000; i++) { new = (alpha*old)%8191; printf("%d \n", new); old = new; } } The main thing to worry about is the line new = (alpha*old)%8191 . Also note that the pseudo random nubers that are generated may not have all the numbers between 0-8191. Also there should be sequence of length around 13 which keeps repeating, for α = 128. The exact sequence depends on the value of α and X (0). 1

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2. <X> n = 1 n n X j =1 X ( j ) = 1 n X ( n )+ n - 1 X j =1 X ( j ) = 1 n X ( n )+( n - 1) 1 n - 1 n - 1 X j =1 X ( j ) = 1 n { X ( n )+( n - 1) <X> n - 1 } = <X> n - 1 + X ( n ) - <X> n - 1 n 3. The students can take the sequence they generate and put it in any plotting software they like. The Fnal value of the average for α = 126 should converge to around 4096
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Unformatted text preview: while that for = 128 should oscillate around. Note that the oscillation for the case of = 128 repeat every 13 values around a value close to 1260. The general shape of the plots is given in igure 1. 2 1000 2000 3000 4000 5000 6000 7000 8000 100 200 300 400 500 600 700 800 900 1000 &quot;ave128&quot; 1000 2000 3000 4000 5000 6000 7000 8000 100 200 300 400 500 600 700 800 900 1000 &quot;ave126&quot; (a) = 128 (b) = 126 1100 1150 1200 1250 1300 1350 1400 1450 1500 100 200 300 400 500 600 700 800 900 1000 &quot;ave128&quot; 3000 3500 4000 4500 5000 100 200 300 400 500 600 700 800 900 1000 &quot;ave126&quot; (a) = 128 (b) = 126 Figure 1: Averages of the random numbers generated for = 128 and = 126. The gures on the bottom row are zoomed versions of the gures on top in order to illustrate the oscillations. 3...
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## This note was uploaded on 09/03/2008 for the course ECSE 4510 taught by Professor Woods during the Spring '03 term at Rensselaer Polytechnic Institute.

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solution01 - while that for = 128 should oscillate around....

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