Question

QUESTION 9

Die Question 2

A regular, i.e., six-faced and balanced, die will be rolled twice. Let the random variable X be equal to the result of subtracting the number obtained on the second roll from the number obtained on the first roll.

Find the variance of X.

a.

2.9167

b.

5.8333

c.

8.75

d.

11.6667

e.

none of the above

Answer 1

X	P(X)	X.P(X)	X².P(X)
-5	1/36 = 0.0278	-0.1389	0.6944
-4	2/36 = 0.0556	-0.2222	0.8889
-3	3/36 = 0.0833	-0.2500	0.7500
-2	4/36 = 0.1111	-0.2222	0.4444
-1	5/36 = 0.1389	-0.1389	0.1389
0	6/36 = 0.1667	0.0000	0.0000
1	5/36 = 0.1389	0.1389	0.1389
2	4/36 = 0.1111	0.2222	0.4444
3	3/36 = 0.0833	0.2500	0.7500
4	2/36 = 0.0556	0.2222	0.8889
5	1/36 = 0.0278	0.1389	0.6944
Total	1	0	5.8333

Variance, σ² = Ʃ(X².P(X)) - μ² = 5.83333333333333 - 0² = 5.8333

Answer B.