You are asked to make a market on the sum of two fair six-sided dice. What is your theoretical value?

Linearity of expectation does the work: $\mathbb{E}[X+Y] = \mathbb{E}[X] + \mathbb{E}[Y] = 3.5 + 3.5 = 7$, and no independence assumption is needed even though the dice happen to be independent. Seven is also the mode and the median here, because the distribution is symmetric about it. The important follow-on is about width rather than centre: the distribution is fully known, so there is no uncertainty in your theo and your market should be tight, perhaps $6.8$ at $7.2$. Quoting a wide market on a known distribution is the error this question is screening for.

Takeaway: On a known distribution your theoretical value is exact, so the market should be tight.