A sequence of random numbers (generated by "the computer", in other words, pseudo random numbers) must be ____________ .

Please choose the option that best fit the empty space above.

Question

A sequence of random numbers (generated by "the computer", in other words, pseudo random numbers) must be ____________ .

Please choose the option that best fit the empty space above.

BlackTom AI · Accepted Answer

Pseudo-random numbers must exhibit no discernible pattern; they should appear random to any statistical test.

1. Relevant knowledge points and concepts
- True randomness vs. pseudo-randomness: computers generate pseudo-random numbers deterministically from a seed, so they are not truly random but should mimic randomness.
- Desirable properties of pseudo-random sequences: uniform distribution (each value equally likely over range), lack of correlation (independence between terms), long period, unpredictability, and absence of discernible patterns.
- Practical requirement: for simulations, cryptography, and sampling the sequence must "look" random — i.e., have no pattern.

2. Step-by-step reasoning
- A computer-generated sequence is deterministic, so to be useful it must pass statistical tests for randomness; otherwise patterns could bias results.
- If a sequence showed a pattern (e.g., repeating blocks, monotonic trends), applications like Monte Carlo simulation or cryptographic keys would be invalid or insecure.
- Therefore the core requirement is that the sequence have no pattern (be patternless or indistinguishable from random).

3. Intermediate steps / illustrative checks
- Uniformity check: histogram should be flat — desirable but not contradictory to "no pattern".
- Autocorrelation check: near zero for nonzero lags — demonstrates lack of correlation/pattern.
- Period check: period should be large so repetition (pattern) doesn’t appear over useable range.

4. Why the correct answer is correct
- "With no pattern" directly captures the essential requirement: pseudo-random sequences must not reveal predictable structure. This is the fundamental practical criterion for usefulness.

5. Why the other options are incorrect
- "Not uniformly distributed": incorrect — we usually want uniformity, not the opposite.
- "Inefficiently generated": irrelevant and undesirable; efficiency is not a must.
- "In descending order": obviously not random.
- "None of the above": incorrect because one option correctly states the requirement.

6. Conclusion
The correct choice is "with no pattern." This matches the provided answer.

A sequence of random numbers (generated by "the computer", in other words, pseudo random numbers) must be ____________ . Please choose the option that best fit the empty space above.单项选择题

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