lista8.doc - FGV/EMAp 2017 Probabilidade 8 Lista de...

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FGV/EMAp – 2017 Probabilidade 8ª Lista de Exercícios 1. O Teorema Central do Limite (para variáveis aleatórias i.i.d) (BJ, p. 240) estabelece que, se X 1 , X 2 , … são variáveis aleatórias independentes e idêntica- mente distribuídas, com média comum e variância comum 2 , então a distribuição de ) ( X n X Var X E X n n S VarS ES S n n n n converge para a distribuição normal padrão (onde S n = X 1 + X 2 + … X n e X = S n / n ). Seja X uma variável aleatória com distribuição binomial de parâmetros n = 100 e p = 0,5. Aplique o T.C.L para obter a distribuição aproximada de
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