In his book "First Certificate Language Practice," Michael Vince says:
Will is used to make predictions. It is often preceded by I think or by opinion words like perhaps. A time expression is also necessary.
I think it'll rain tomorrow.
My impression is that, if placed at the end of the sentence, "I expect" sounds like an afterthought and is introduced to soften the prediction. If "going to" is used, the meaning is similar. The only difference is that, when placed at the beginning, "I expect/think/believe" will tend to be followed by "will" at all times.
Y. John will win the match tomorrow, I expect.
Z. John is going to win the match tomorrow, I expect. (...actually, I expect he will.)
See what Vince says in connection with "going to":
Going to is also used for predictions. It is especially common when we can see the cause of the event.
Look out! There's a bus coming! It's going to hit us!
I can see you're going to have a baby. When is it due?
You're going to fall!
Going to is also common in impersonal statements.
Liverpool are going to win the Cup. But will can also be used for most examples like this, with no change of meaning. (The bolds are mine.)
See the similarity between the example above and the one from your book in which, as David told you, both "will" and "is going to" can be used unless "I expect" appears at the beginning, in which case "I will" is preferred.