4 fair dice are rolled. Find the expected total of the rolls.

Question

I'm using expectation in this problem

If the expected value of 1 roll is:

E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)

= 1/6(1+2+3+4+5+6)

= 21/6

= 7/2

Then would the expected total of 4 rolls be:

7/2 * 4 = 14?

Answer 1

Yes that is the expected total. As pointed out in the comments, the expectation of a sum the sum of the expectations so you can just straight-up sum them.