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ociaw/BiasedRng.csx

Created May 28, 2020
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Demonstrates the high amount of bias in .NET's random number generator, System.Random.
var rng = new Random(42);
var sampleSize = 10_000_000;
var numbers = Enumerable.Repeat(0, sampleSize).Select(_ => rng.Next(0, Int32.MaxValue));
var heads = numbers.Count(x => x % 2 == 1);
Console.WriteLine($"Heads: {heads}, tails: {sampleSize - heads}");
// Output: Heads: 5,036,860, tails: 4,963,140
var popStdDev = Math.Sqrt(0.5 * 0.5);
var popMean = 0.5;
var sampleMean = (Double)heads / sampleSize;
var difference = popMean - sampleMean;
var z = difference * Math.Sqrt(sampleSize) / popStdDev;
Console.WriteLine($"Z score: {z}");
// Output: Z score: -23.3123109107611
// According to my calculator, the probably of this occurring is 0.
// Wolfram Alpha is a bit more precise, giving me 3.326*10^-120.
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