Question

Consider the experiment consisting of throwing a die twice, so the sample space is Ω = {(ω1, ω2)|ω1, ω2 ∈ {1, 2, . . . , 6}}. Let D be the random variable giving the difference between the outcome of the first throw and the outcome of the second throw, D((ω1, ω2)) = ω1−ω2. Sketch the graph of the probability mass function and the graph of the distribution function of D.

Answer 1

X1	X2	D
1	1	0
2	1	1
3	1	2
4	1	3
5	1	4
6	1	5
1	2	-1
2	2	0
3	2	1
4	2	2
5	2	3
6	2	4
1	3	-2
2	3	-1
3	3	0
4	3	1
5	3	2
6	3	3
1	4	-3
2	4	-2
3	4	-1
4	4	0
5	4	1
6	4	2
1	5	-4
2	5	-3
3	5	-2
4	5	-1
5	5	0
6	5	1
1	6	-5
2	6	-4
3	6	-3
4	6	-2
5	6	-1
6	6	0

D	n	p
-5	1	0.027778
-4	2	0.055556
-3	3	0.083333
-2	4	0.111111
-1	5	0.138889
0	6	0.166667
1	5	0.138889
2	4	0.111111
3	3	0.083333
4	2	0.055556
5	1	0.027778
	36	1

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