Here is a valid solution:
For i = 1, 2, ..., 6
Xi be the random variable that counts the number of times that i came out.
Let X be the sum of n dices. X = 1*X1 + 2*X2 + ... + 6*X6
E(Xi) = n/6
E(X) = E(1 * X1 + 2 * X2 + ... + 6 * X6) =
1 * E(X1) + 2 * E(X2) + ... + 6 * E(X6) =
1 * (n/6) + 2 *...
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