Question 1

What is the difference between pseudo-random and true random?

Accepted Answer

Pseudo-random number generators (PRNGs) are deterministic algorithms that produce sequences appearing statistically random but fully reproducible from a starting seed. The Mersenne Twister MT19937 (Matsumoto and Nishimura 1998, ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, pp. 3-30) has a period of 2^19937 - 1 and is the default in Python's `random` module, C++ `std::mt19937`, and Ruby. JavaScript `Math.random()` in the V8 engine (Chrome, Node.js) uses xorshift128+ per V8 blog December 2015. True random number generators (TRNGs) draw from physical entropy sources: thermal noise (Intel RDRAND/RDSEED per Intel Digital Random Number Generator Software Implementation Guide), radioactive decay (HotBits), or atmospheric noise (random.org). NIST Special Publication 800-90A Rev. 1 specifies deterministic random bit generator (DRBG) algorithms; SP 800-90B specifies entropy source validation testing; SP 800-90C specifies DRBG constructions.

Question 2

What is the difference between Math.random() and crypto.getRandomValues() in JavaScript?

Accepted Answer

`Math.random()` returns a pseudo-random float in [0, 1) using a fast non-cryptographic PRNG - V8 (Chrome, Node.js) uses xorshift128+; SpiderMonkey (Firefox) uses xorshift128+; JavaScriptCore (Safari) uses a custom PRNG. `Math.random()` MUST NOT be used for security applications (password generation, cryptographic keys, session tokens, CSRF tokens, or lottery draws), per MDN Web Docs. `crypto.getRandomValues()` from the Web Crypto API (W3C Recommendation 26 January 2017) fills a typed array with cryptographically secure random bytes drawn from OS entropy sources - /dev/urandom on Linux and macOS, BCryptGenRandom on Windows since Windows 10 per Microsoft Docs. For UUIDs use `crypto.randomUUID()` (Web Crypto API extension standardized 2021). Node.js provides `crypto.randomBytes()` and `crypto.randomInt()` since Node 14.10 for server-side use.

Question 3

How do I generate a random integer in a specific range without bias?

Accepted Answer

Naive approach for uniform integer in [min, max] inclusive: `Math.floor(Math.random() * (max - min + 1)) + min` - acceptable for non-security use but subtly non-uniform because the PRNG output is not a perfect multiple of the range. For cryptographically-secure unbiased generation, use rejection sampling: draw random bytes with `crypto.getRandomValues(new Uint32Array(1))[0]`, compute the largest multiple of the range that fits in 2^32, and reject values above that threshold - re-drawing until acceptance. This avoids modulo bias per NIST SP 800-90A §9.1 (Random Number Generation Using Deterministic Random Bit Generators). Python: `random.randint(min, max)` for PRNG use; `secrets.randbelow(range) + min` for cryptographically-secure use (PEP 506, Python 3.6+). C++11: `std::uniform_int_distribution<int>(min, max)(gen)` with `std::random_device` or `std::mt19937`.

Question 4

What is a random seed and why does it matter for reproducibility?

Accepted Answer

A seed is the initial internal state supplied to a PRNG; the same seed always produces the same output sequence. Setting `random.seed(42)` in Python's `random`, `np.random.seed(42)` in NumPy, or `torch.manual_seed(42)` in PyTorch enables reproducible scientific computing - a core requirement of the FAIR (Findable, Accessible, Interoperable, Reusable) Data Principles per Wilkinson et al. 2016 Scientific Data 3, article 160018. Machine-learning reproducibility requires seeding every source of randomness: Python built-in `random`, NumPy, PyTorch (CPU and CUDA), TensorFlow, and disabling non-deterministic CUDA kernels via `torch.use_deterministic_algorithms(True)` per PyTorch Reproducibility Notes. For lotteries, gambling, or cryptographic applications, seeding is undesirable; instead use a Cryptographically-Secure PRNG (CSPRNG) seeded from OS entropy sources that remain hidden from adversaries.

Question 5

What are the common applications of random number generation?

Accepted Answer

Random numbers underpin many computing and statistical applications: (1) lotteries and drawings - Powerball and Mega Millions use certified mechanical drawing machines per Multi-State Lottery Association (MUSL) rules, and state lotteries follow NIST-validated RNG hardware per state gaming commission audits; (2) Monte Carlo simulation - Metropolis and Ulam (1949, Journal of the American Statistical Association, Vol. 44, No. 247, pp. 335-341, 'The Monte Carlo Method') is the founding paper, developed at Los Alamos for neutron transport calculations; (3) cryptographic key generation - AES-256 requires 256 bits of entropy per NIST FIPS 197 (Announcing the Advanced Encryption Standard, 2001); (4) statistical sampling - Simple Random Sampling Without Replacement (SRSWOR) per Cochran, 'Sampling Techniques' (3rd edition, 1977); (5) video games (procedural generation, loot drops, damage rolls); (6) password generation per NIST SP 800-63B; (7) A/B testing and Bayesian experimentation per Kohavi, Tang, and Xu, 'Trustworthy Online Controlled Experiments' (Cambridge University Press 2020).