位置13的问题 A property of the Poisson distribution is that the mean equals the 题库 1/1[input].

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BlackTom AI · Accepted Answer

Consider the statement about the Poisson distribution in the question. The blank is asking to fill in with the quantity that the mean equals in a Poisson distribution.
In a Poisson distribution with parameter λ, the mean is E[X] = λ and the variance is Var[X] = λ as well. This is a defining property: the two moments coincide and equal the rate parameter λ.
Therefore, the blank should be filled with the term that represents this shared value, namely 'variance'.
A common point of confusion is to mix up standard deviation with variance; while the standard deviation is sqrt(λ), it is not equal to the mean, and the Poisson moments are both λ for mean and variance, not the standard deviation.
Another potential misconception is thinking Poisson properties only involve the mean. In fact, the variance is equally tied to the same parameter, reinforcing the equality of mean and variance in this distribution.
If someone considers alternative descriptions, they might recall that adding independent Poisson counts yields another Poisson count with summed rates, which also relies on the same λ parameter for both mean and variance, reinforcing why variance is the appropriate completion here.

位置13的问题 A property of the Poisson distribution is that the mean equals the 题库 1/1[input].

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