#1 (Quality of Random Number Generator) We all know Fibonacci sequence, which is defined by the...
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#1 (Quality of Random Number Generator) We all know Fibonacci sequence, which is defined by the following recurrence relation: Zo = 0, Z = 1, Zn = Zn-1 + Zn-2 Vn>1. This sequence was used to generate pseudo-random numbers in history, named the Fibonacci generator: Zi Z = (Zi-1 + Zi-2) mod m, but it has serious deficiencies, as you can prove in the following two parts. (a) Show that this generator can never produce the following arrangement of three consec- utive output values: U-2 < U < Ui-1 (b) Show that the arrangement in part (a) should occur with probability for a "perfect" random-number generator. #1 (Quality of Random Number Generator) We all know Fibonacci sequence, which is defined by the following recurrence relation: Zo = 0, Z = 1, Zn = Zn-1 + Zn-2 Vn>1. This sequence was used to generate pseudo-random numbers in history, named the Fibonacci generator: Zi Z = (Zi-1 + Zi-2) mod m, but it has serious deficiencies, as you can prove in the following two parts. (a) Show that this generator can never produce the following arrangement of three consec- utive output values: U-2 < U < Ui-1 (b) Show that the arrangement in part (a) should occur with probability for a "perfect" random-number generator.
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Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
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