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Windows - vault backup: 2024-12-21 15:32:30
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Secondo Anno/Primo Semestre/Calcolo delle Probabilità.md
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alem1105 committed Dec 21, 2024
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6 changes: 3 additions & 3 deletions Secondo Anno/Primo Semestre/Calcolo delle Probabilità.md
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$X_{1},X_{2},\dots,X_{n}$ sono v.a. I.I.D., cosa significa?
- Indipendenti significa che $\forall n$ $X_{1},\dots,X_{n}$ sono indipendenti, ovvero:

$$
P(X_{1}\in A_{1}, \dots, X_{n}\in A_{n}=\prod_{i=1}^n P(X_{i}\in A_{i}) \quad \forall A_{1},\dots,A_{n} \subset \mathbb{R}
$$
$$
P(X_{1}\in A_{1}, \dots, X_{n}\in A_{n}=\prod_{i=1}^n P(X_{i}\in A_{i}) \quad \forall A_{1},\dots,A_{n} \subset \mathbb{R}
$$

- Identicamente Distribuite significa che $\forall i\neq j$ vale $P(X_{i}\in A)=P(X_{j}\in A) \quad \forall A\subset \mathbb{R}$, quindi non le distinguiamo a livello probabilistico.

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