If P is the mean of Poisson distribution, then what is the standard deviation?

To determine the standard deviation of a Poisson distribution when given the mean, we rely on the core properties of this probability distribution.

Understanding Poisson Distribution Parameters
In a Poisson distribution, there is a single parameter, often denoted by the Greek letter λ (lambda), which represents both the mean and the variance of the distribution.

Mean: In this problem, the mean is given as P. Therefore, Mean = P.

Variance: A defining characteristic of the Poisson distribution is that the variance is equal to the mean. Therefore, Variance = P.

Standard Deviation: The standard deviation is defined as the square root of the variance.

Since Variance = P, it follows that:
Standard Deviation = √P