If a set of values exhibits a Poisson distribution with a mean value of 1, then the probability of observing no successes in a given period is equal to 0.368. (Note: The value of e = 2.718.)

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Quizplus · Accepted Answer

The probability of observing no successes in a Poisson distribution is given by $P(X=0) = e^{-\lambda}$, where $\lambda$ is the mean number of successes. For $\lambda = 1$, $P(X=0) = e^{-1} = \frac{1}{e} \approx \frac{1}{2.718} \approx 0.368$.

If a Set of Values Exhibits a Poisson Distribution with a Mean