A fair die is rolled ten times. Find numerical values for the expectations of each of the following random variables

1. the sum of the numbers in the ten rolls;
2. the sum of the largest two numbers in the first three rolls;
3. the maximum number in the first five rolls;
4. the number of multiples of three in the first ten rolls;
5. the number of faces which fail to appear in the ten rolls;
6. the number of different faces that appear in the ten rolls.

[From Pitman page 183]