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  "body": "\n## Summary\n\nMathematical statistics is the part of mathematics that studies how to learn about an unknown probability distribution from data.\nIt models data as the values of random variables whose law belongs to a [[statistical model|JZ6R7J36K5]].\nIt then studies procedures such as estimators, tests and confidence sets through their behaviour under each law of the model.\nIt gives the rigorous basis for [[statistical inference|FXCQWFY5RV]].\n\n## Explanations\n\n### L1 human\n\nData are noisy, so a conclusion drawn from data can be wrong.\nMathematical statistics uses probability theory to measure how often a method of drawing conclusions goes wrong.\nPicture a coin with an unknown chance $p$ of heads, tossed $100$ times.\nThe proportion of heads is a natural guess for $p$, and mathematical statistics tells how far this guess typically lies from $p$: about $\\sqrt{p(1-p)/100}$, at most $0.05$.\n",
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