Front: What are the three ideal properties of a Random Number Generator (RNG)?
Back: Repeatability, long cycle length, and high speed.
Front: Why is repeatability important in an RNG?
Back: It allows generating the same sequence of numbers using a seed, which is critical for testing and debugging.
Front: What is the significance of a long cycle length in an RNG?
Back: It ensures the sequence remains random for a large number of values before repeating or becoming predictable.
Front: Why would a true RNG be unsuitable for scenarios requiring reproducibility?
Back: True RNGs lack a seed, making them inherently non-repeatable due to reliance on unpredictable physical processes.
Front: Name two physical processes used to generate true random numbers.
Back: Quantum phenomena or radioactive decay.
Front: What statistical property do true RNGs exhibit within an interval?
Back: Uniform distribution (equal count of each number in the interval).
Front: List three benefits of computational (pseudo) RNGs over true RNGs.
Back: Repeatability, portability across systems, and approximation of statistical properties like uniformity and independence.
Front: What is a major drawback of many pre-installed PRNGs in computer systems?
Back: Short cycle lengths and strong correlation patterns in generated sequences.
Front: What is the recurrence relation for a Linear Congruential Generator (LCG)?
Back: , where are integers.
Front: How does a mixed congruential method differ from a multiplicative congruential method?
Back: Mixed uses , while multiplicative sets .
Front: What parameters does Numerical Recipes recommend for an LCG?
Back: , , .
Front: What is the maximum possible period of an LCG sequence?
Back: At most (the modulus value), but it can be shorter depending on constants and seed.
Front: Why are PRNGs considered “random enough” for statistical applications?
Back: They closely approximate uniformity and independence in generated sequences.
Front: What key trade-off exists for PRNGs like LCGs?
Back: Speed vs. cycle length and correlation issues (fast but shorter cycles).