hw3_solns_cont - ORIE 4580/5580/5581 Solutions for Homework...

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ORIE 4580/5580/5581 Solutions for Homework Assignment 3 Question 3. A set of 50 trial runs indicates that we should choose N = 683. (You may observe a different value, due to randomness.) 683 production runs yield the confidence interval [3 . 270 , 3 . 363]. (You may observe a different value, due to randomness.) See the accompanying spreadsheet. Question 4. a) In order to ensure that the LCG has full period, we use Theorem 1 in the lecture notes “Generating Samples of Uniformly Distributed Random Variables.” We pick m = 12 6 . Since m = 12 6 = 2 12 3 6 , the only prime numbers that divide m are 2 and 3. In order to satisfy the Condition 1, we have to select c such that c is not a multiple of 2 or 3. We pick c = 5 4 = 625( > 500). Since the only prime numbers that divide m are 2 and 3, in order to satisfy Condition 2, we have to make sure that 2 and 3 divides a - 1. Finally, to satisfy Condition 3, since 4 divides m , we have to make sure that 4 divides a - 1. Thus, 2, 3 and 4 have to divide a - 1. Picking
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