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  "body": "\n## Definition\n\nLet $(X_i)_{i \\in I}$ be a family of random variables on one probability space, all with values in the same measurable space $(E, \\mathcal{E})$.\nThe family is independent and identically distributed (i.i.d.) if both of these conditions hold:\n1. The family $(X_i)_{i \\in I}$ is [[independent|0XCE070V8B]].\n2. The random variables $X_i$ are [[identically distributed|01X8YSDTBW]]: all $X_i$ have the same law $\\mu$.\n\n## Remarks\n\nOne also says that $X_1, X_2, \\dots$ is an i.i.d. sequence with common law $\\mu$, or a random sample from $\\mu$.\nThe results of repeated tosses of one coin form an i.i.d. sequence of Bernoulli random variables.\nThe law of large numbers and the central limit theorem are first proved for i.i.d. sequences.\n\n## Explanations\n\n### L1 human\n\nI.i.d. variables are the results of the same experiment, repeated under the same conditions, with no influence between the repetitions.\nEach one follows the same law, and none of them gives information about the others.\n",
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