In the Poisson distribution if P(x = k) = P(x = k+1) for some positive integer k, then the mean isGroup of answer choices2k-1k+1kk-1

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space. The probability mass function of a Poisson distribution is given by:

P(X=k) = λ^k * e^-λ / k!

where λ is the average rate of value (or the mean), k is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.

Given that P(X=k) = P(X=k+1), we can set up the following equation using the probability mass function:

λ^k * e^-λ / k! = λ^(k+1) * e^-λ / (k+1)!

Solving this equation for λ gives us the mean of the Poisson distribution.

First, simplify the equation:

λ^k / k! = λ^(k+1) / (k+1)!

This simplifies to:

1/k = λ

So, the mean λ is equal to k. Therefore, the correct answer is k.