6.1.2—The fact that if X Po+

For X~Po(λ), E(X)=λ and Var(X)=λ. For a time or area interval scaled by k, the mean becomes kλ under a constant-rate model.

Use the equality as a model check, not as a statement that every sample has equal mean and variance. Estimate λ from appropriate exposure.

If the observed average is 4 events per hour, a two-hour interval has Po(8), not Po(4).

Sample variance need not equal sample mean exactly; the equality describes the distributional parameter.