Expected value of the sum of $n$ dice rolls.

Question

We roll a dice exactly $n$ times. What is the expected value of the sum of the outocomes?

I have given this problem some thought, but I don't know how to tackle this. The problem is, that each sum has a different probability of coming out. For example, there is only one way to achieve the sum $6n$, $5n$ etc, but more than one way to achieve $4n + 4$.

Is there a clever way to tackle this?

Answer 1

Because of the linearity of expectations, the expectation of $n$ dice rolls is simply $n\times E(X)$ where $E(X)$ is the expectation of a single die.