X is the sum of rolled amounts after throwing dice 500 times. Average value of dots in single throw is 3.5. What is expected value of this event?

Question

$X$ is the sum of rolled amounts after throwing dice $500$ times. Average value of dots in single throw is $3.5$. What is expected value of this event?

Isn't this just $$500\times 3.5=1750 \,?$$

Sorry if it's too simple, this task is highly rated on test so it makes me doubt my answer... Is this correct?

Answer 1

Assuming that the events are independent, let $X_k$ denote the $k$-th roll. Then, \begin{align} E[X_1+X_2 +\dots +X_{500}]=E[500 \cdot X_1] = 500E[X_1] \end{align} by independence and linearity of expectation.