8 Exercises

• Exercise 1: Buffon's Needle Problem, to illustrate geometrically some of the properties of random numbers.
• Exercise 2: Illustrate the mean and variance of uniformly distributed random numbers.
• Exercise 3: Illustrate the generation of random numbers using LCG(13445, 0, 65536, 16811) and to partition the random real numbers into bins.
• Exercise 4: Establish all cycles in LCGs when m = p, at a prime.
• Exercise 5: Exploring all possible sequences in simple LCGs.
• Exercise 6: Cray's LCG ranf()
• Exercise 7: Visualization of some poor LCGs.
• Exercise 8: Vectorization of Cray's LCG.
• Exercise 9: Leap-ahead in an LCG.
• Exercise 10: Explore LFGs visually.
• Exercise 11: The fundamental concepts of LFGs.
• Exericise 12: Various LFGs as they influence the number and length of cycles.