Consider the Fibonacci generator discussed in Sec. 7.3.1.(a) Show that this generator can...

Consider the Fibonacci generator discussed in Sec. 7.3.1.

(a) Show that this generator can never produce the following arrangement of three consecutive output values: U_{i – 2} < U_i < U_{i – 1}.

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(b) Show that the arrangement in (a) should occur with probability  for a “perfect” random-number generator.

This points out a gross defect in the generator, as noted by Bratley, Fox, and Schrage (1987), who credit U. Dieter with having noticed this.