Suppose a fair die is rolled ten times. Find numerical values for the expectations of each of the following random variables:
a) The sum of the numbers in the ten rolls:
b) The sum of the largest two numbers in the first three rolls:
c) The maximum number in the first five rolls:
d) The number of multiples of three in the ten rolls:
e) The number of faces which fail to appear in the ten rolls:
f) The number of different faces that appear in the ten rolls: