Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows: 1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2

Which of the following statement is correct?

a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one