When there are two parts to a sentence, one a statement and one a question, it is the part at the end that determines the terminal punctuation.
...My question is where are you going?
...Where are you going? is my question.
In the second example, since the sentence ends in a period, there has to be a question mark mid-sentence at the end of the question.
This is another way to put it: In the second sentence the whole question is actually the subject of the sentence. The word "question" is the predicate nominative. The insertion of the question mark mid-sentence is because that is where the question is being asked. The end of the statement is a question and needs a period.
Happy punctuating!
Margie