Question

A pair of dice is tossed.

Calculate the variance of the sum of the dice?

A) 35/6

B) 37/6

C) 6

D) 19/3

E) 17/3

Answer 1

A pair of dice is rolled; let X be the sum of the two numbers that appear

outcome	X	P(X)
(1,1)	2	1/36
(1,2)(2,1)	3	2/36
(1,3)(3,1)(2,2)	4	3/36
(1,4)(4,1)(2,3)(3,2)	5	4/36
(1,5)(5,1)(2,4)(4,2)(3,3)	6	5/36
(1,6)(6,1)(2,5)(5,2)(3,4)(4,3)	7	6/36
(2,6)(6,2)(3,5)(5,3),(4,4)	8	5/36
(3,6)(6,3)(4,5)(5,4)	9	4/36
(4,6)(6,4)(5,5)	10	3/36
(5,6)(6,5)	11	2/36
(6,6)	12	1/36

X	P(X)	X*P(X)	X² * P(X)
2	0.0278	0.0556	0.1111
3	0.0556	0.1667	0.5000
4	0.0833	0.3333	1.3333
5	0.1111	0.5556	2.7778
6	0.1389	0.8333	5.0000
7	0.1667	1.1667	8.1667
8	0.1389	1.1111	8.8889
9	0.1111	1.0000	9.0000
10	0.0833	0.8333	8.3333
11	0.0556	0.6111	6.7222
12	0.0278	0.3333	4.0000

	P(X)	X*P(X)	X² * P(X)
total sum =	1	7	54.83

mean = E[X] = Σx*P(X) =            7.00000
          
E [ X² ] = ΣX² * P(X) =            54.8333
          
variance = E[ X² ] - (E[ X ])² = 5.8333 = 35/6

answer: 35/6