Question

A) What is the mean value of the sum of three independent dice throws?

B) What is the variance of the sum of two independent dice throws?

Answer 1

A) What is the mean value of the sum of three independent dice throws?

1 possible way three dice can total 3
3 ways for 4
6 for 5
10 for 6
15 for 7
21 for 8
25 for 9
27 for 10
27 for 11
25 for 12
21 for 13
15 for 14
10 for 15
6 for 16
3 for 17
1 for 18

Thus, we get

sum	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
count	1	3	6	10	15	21	25	27	27	25	21	15	10	6	3	1

Mean = (sum*count) for each row / total count

= (3*1 + 4*3 + ... + 18*1) / (1+3+6+..+1)

solving we get

Mean = 2268/216

= 10.5

B) What is the variance of the sum of two independent dice throws?

- Rolling one dice has variance of (35/12)

For two independent dice throws variance = 2*(35/12)

= 5.83