For any i from 1 to p+q-1,
This is also .
The number we want, the average number of change points, is
. There is an extremely useful theorem saying that if X and Y are random variables then E(X+Y) = E(X) + E(Y). It's important to note that it is not necessary that X and Y be independent in order to apply this theorem. This good for us because the are not independent. So let's apply it as follows:
Hope this helps-- I'm in a rush, but then so are you.