The roll of a pair of dice has the following probability distribution, where the random variable x is the sum of the values produced by each die:
x P(x)
2………………………1/36
3………………………2/36
4……………………...3/36
5……………………...4/36
6……………………...5/36
7……………………...6/36
8……………………...5/36
9……………………...4/36
10…………………….3/36
11…………………….2/36
12…………………….1/3
a. Calculate the expected value of x.
b. Calculate the variance of x.
c. Calculate the standard deviation of x.