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Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.

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Answer to a math question Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.

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Para determinar a probabilidade de X ser no máximo 2, onde X tem uma distribuição de Poisson com média de 0,4, podemos usar a fórmula da função de massa de probabilidade de Poisson. A fórmula é P(X = k) = \frac} onde λ é a média da distribuição de Poisson ek é o número de ocorrências do evento. Neste caso, λ = 0,4 e queremos encontrar P(X ≤ 2), que é o mesmo que P(X = 0) P(X = 1) P(X = 2). Usando a fórmula, temos P(X = 0) = \frac} = \frac = 0,67032 P(X = 1) = \frac} = \frac = 0,26813 P(X = 2) = \frac} = \frac = 0,05363 Portanto, P(X \leq 2) = P(X = 0) P(X = 1) P(X = 2) = 0,67032 0,26813 0,05363 = 0,99208 Portanto, a probabilidade de X ser no máximo 2 é de aproximadamente 0,99208.

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