#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.