Question

Can you combine IID Poisson variables?

A. Yes, always
B. No, never
C. Yes, only if means are equal
D. Yes, only if variances are equal

Answer 1

When combining IID Poisson variables, the answer depends on whether the variances are equal or not.

Step-by-step explanation:

When combining independent and identically distributed (IID) Poisson variables, the resulting variable will still be a Poisson variable with a mean equal to the sum of the individual means. The variance of the combined variable is also equal to the sum of the individual variances. Therefore, the answer is D. Yes, only if variances are equal.