If I have a question such as:

P(X(1) = 2,X(3) = 12) with Poisson Distribution X - Po(4)

Would I be right in saying this is the same as:

P(X(1) = 2,X(3) - X(1) = (12-3))

=

P(X(1) = 2,X(2) = 9)?

Thank in advance

Craig