Chapter 7.5, Problem 19E

Dice The probability distribution for the sum of numbers obtained from rolling a pair of dice is given in Table 9.

(a) Compute the mean and the variance of this probability distribution.

(b) Using the table, give the probability that the number is between 4 and 10, inclusive.

(c) Use the Chebychev inequality to estimate the probability that the number is between 4 and 10, inclusive.

Table 9

Sum	Probability
2	$\frac{1}{36}$
3	$\frac{2}{36}$
4	$\frac{3}{36}$
5	$\frac{4}{36}$
6	$\frac{5}{36}$
7	$\frac{6}{36}$
8	$\frac{5}{36}$
9	$\frac{4}{36}$
10	$\frac{3}{36}$
11	$\frac{2}{36}$
12	$\frac{1}{36}$

Table 10

Ones	Probability
0	.112
1	.269
2	.296
3	.197
4	.089
5	.028
6	.007
7	.001
8	.000
9	.000
10	.000
11	.000
12	.000