Consider the following family of distributions P P(X x) P(X x) xe x x 0, 1, 2, 0 or 1 This is a Poisson family with restricted to be 0 or 1 Show that the family P is not complete, demonstrating that completeness can be dependent on the range of the parameter ...

If 0 EhX h0 If 1 Let h0 0 an ...

Consider the following family of distributions: P = {P(X = x): P(X = x) = xe- /

Question:

Consider the following family of distributions:
P = {Pλ(X = x): Pλ(X = x) = λxe-λ / x!; x = 0, 1, 2,...; λ = 0 or 1}.
This is a Poisson family with λ restricted to be 0 or 1. Show that the family P is not complete, demonstrating that completeness can be dependent on the range of the parameter.