1. 0 3
0 10
0 12
0 25
0 39
0 50
0 74
0 76
0 84
0 87
0 89
0 96
1 4
1 10
1 13
1 25
1 29
1 31
1 33
1 35
1 74
1 82
2 3
2 4
2 31
2 38
2 42
2 44
2 49
2 66
2 73
2 75
2 93
3 4
3 12
3 17
3 24
3 30
3 31
3 33
3 53
3 71

2. 3 94
4 3
4 21
4 24
4 37
4 46
4 58
4 60
4 79
4 81
4 93
4 97
5 6
5 35
5 89
5 96
6 30
6 33
6 35
6 50
6 62
6 80
7 35
7 41
7 51
7 71
7 74
7 77
7 79
7 81
7 88
7 94
8 1
8 34
8 59
8 61
8 63
8 66
8 67
8 82
9 10
9 21

3. 9 27
9 29
9 38
9 45
9 48
9 52
9 61
9 65
9 84
9 86
9 93
10 7
10 21
10 52
10 61
10 83
10 99
11 1
11 19
11 25
11 36
11 42
11 52
11 54
11 56
11 59
11 77
11 83
11 84
11 90
11 94
11 98
12 2
12 10
12 27
12 28
12 37
12 42
12 65
12 80
12 90
12 94

4. 12 98
13 3
13 21
13 26
13 35
13 39
13 40
13 50
13 53
13 66
13 74
13 77
13 81
13 84
13 97
14 0
14 20
14 28
14 48
14 52
14 55
14 57
14 70
14 78
14 88
14 91
14 92
14 95
15 8
15 11
15 12
15 29
15 34
15 41
15 71
15 89
15 90
16 18
16 21
16 36
16 74
16 83

5. 16 92
17 1
17 5
17 8
17 10
17 18
17 28
17 29
17 32
17 33
17 45
17 52
17 55
17 57
17 60
17 65
17 80
17 87
17 88
17 98
18 5
18 6
18 16
18 23
18 25
18 32
18 44
18 58
18 86
18 93
18 96
19 8
19 10
19 19
19 31
19 39
19 50
19 53
19 74
19 81
19 84
19 85

6. 19 94
20 11
20 29
20 34
20 49
20 63
20 71
20 79
20 83
20 89
20 98
20 99
21 4
21 19
21 23
21 37
21 52
21 63
21 69
21 70
21 96
22 2
22 19
22 46
22 58
22 59
22 64
22 74
22 75
22 78
22 83
22 86
23 7
23 24
23 30
23 76
23 98
24 0
24 5
24 11
24 27
24 35

7. 24 45
24 59
24 61
25 12
25 21
25 61
25 72
25 73
25 90
25 93
26 0
26 2
26 13
26 20
26 24
26 36
26 46
26 47
26 48
26 50
26 62
26 63
26 91
27 7
27 25
27 31
27 53
27 60
27 65
27 72
27 76
27 79
27 89
28 6
28 41
28 43
28 64
28 67
28 85
28 95
29 0
29 21

8. 29 39
29 47
29 48
29 53
29 66
29 71
29 77
29 78
29 79
29 81
29 89
29 98
30 3
30 4
30 5
30 24
30 31
30 61
30 74
30 77
30 85
30 97
31 30
31 36
31 77
31 78
31 79
32 8
32 16
32 20
32 42
32 57
32 68
32 69
32 90
33 12
33 15
33 29
33 32
33 48
33 52
33 61

9. 33 82
33 98
34 5
34 15
34 35
34 40
34 49
34 50
34 67
34 68
34 87
35 4
35 8
35 15
35 19
35 25
35 34
35 48
35 68
35 82
35 93
35 94
36 20
36 33
36 36
36 44
36 57
36 66
36 67
36 71
36 80
36 85
36 89
36 95
37 19
37 39
37 44
37 51
37 69
37 75
37 81
37 85

10. 37 89
37 92
38 8
38 16
38 20
38 24
38 39
38 71
38 78
38 96
39 16
39 27
39 30
39 36
39 39
39 46
39 51
39 67
39 87
39 94
39 95
40 17
40 18
40 19
40 26
40 34
40 40
40 41
40 45
40 53
40 55
40 70
40 71
40 76
40 86
41 1
41 2
41 4
41 13
41 23
41 25
41 38

11. 41 51
41 52
41 73
42 7
42 17
42 19
42 24
42 26
42 31
42 33
42 35
42 45
42 47
42 78
42 93
42 94
43 0
43 1
43 10
43 13
43 28
43 49
43 61
43 67
43 68
43 99
44 13
44 27
44 35
44 47
44 62
44 68
44 79
44 84
44 85
44 87
45 10
45 19
45 20
45 21
45 26
45 38

12. 45 39
45 43
45 48
45 49
45 73
45 76
45 82
45 85
45 86
45 96
46 6
46 14
46 43
46 69
46 93
47 10
47 11
47 12
47 17
47 37
47 40
47 42
47 59
47 64
47 74
48 43
48 45
48 46
48 71
48 75
49 2
49 3
49 9
49 10
49 11
49 28
49 31
49 32
49 36
49 38
49 53
49 59

13. 49 60
49 62
49 85
49 91
50 4
50 6
50 13
50 21
50 23
50 45
50 77
50 79
50 80
50 98
51 4
51 15
51 18
51 46
51 63
52 2
52 5
52 14
52 23
52 25
52 30
52 56
52 57
52 64
52 65
52 74
52 95
52 99
53 15
53 29
53 30
53 41
53 42
53 47
53 56
53 74
53 94
54 60

14. 54 73
54 81
54 95
54 97
55 43
55 50
55 60
55 71
55 84
55 87
55 88
56 18
56 26
56 28
56 39
56 51
56 52
56 57
56 63
56 77
56 84
56 88
56 98
57 11
57 17
57 36
57 43
57 44
57 48
57 50
57 54
57 60
57 61
57 62
57 69
57 70
57 77
57 88
57 89
57 90
58 10
58 19

15. 58 26
58 41
58 57
58 79
59 0
59 17
59 26
59 31
59 50
59 69
59 80
59 81
60 9
60 13
60 36
60 37
60 43
60 67
60 93
61 16
61 21
61 46
61 83
61 97
61 99
62 11
62 16
62 18
62 24
62 33
62 47
62 65
62 73
62 90
62 99
63 13
63 20
63 23
63 29
63 36
63 37
63 41

16. 63 55
63 61
63 69
63 76
63 78
63 82
63 86
63 97
63 99
64 25
64 29
64 30
64 39
64 52
64 53
64 64
64 67
64 69
64 86
64 91
64 93
64 96
64 97
65 8
65 9
65 42
65 46
65 51
65 55
65 58
65 59
65 64
65 72
65 73
65 80
65 81
65 97
66 0
66 11
66 18
66 23
66 40

17. 66 51
66 64
66 69
66 70
66 83
66 95
66 96
67 11
67 26
67 59
67 75
67 80
67 87
68 8
68 18
68 21
68 26
68 45
68 48
68 63
68 98
69 12
69 22
69 26
69 36
69 42
69 67
69 76
69 77
69 81
69 88
69 91
70 1
70 11
70 14
70 20
70 22
70 41
70 60
70 61
70 79
70 82

18. 70 91
70 93
70 99
71 3
71 14
71 18
71 33
71 43
71 45
71 92
71 95
71 98
72 1
72 11
72 50
72 59
72 66
72 74
72 78
72 97
72 98
73 1
73 11
73 13
73 27
73 28
73 39
73 45
73 51
73 57
73 60
73 61
73 74
74 9
74 32
74 56
74 64
74 76
74 83
74 97
75 1
75 3

19. 75 32
75 36
75 43
75 59
75 63
75 83
75 95
76 8
76 12
76 29
76 37
76 46
76 56
76 64
76 76
76 83
76 89
76 96
76 99
77 9
77 12
77 15
77 27
77 28
77 29
77 35
77 42
77 45
77 79
77 81
77 88
78 29
78 42
78 53
78 57
78 58
78 67
79 3
79 7
79 12
79 14
79 25

20. 79 37
79 51
79 71
79 74
79 76
79 85
80 6
80 22
80 30
80 48
80 63
80 81
80 85
80 90
81 7
81 16
81 18
81 19
81 28
81 33
81 38
81 40
81 45
81 46
81 78
81 85
81 94
81 96
82 12
82 30
82 36
82 37
82 38
82 42
82 44
82 53
82 56
82 65
82 81
82 85
82 93
83 2

21. 83 5
83 13
83 16
83 19
83 28
83 41
83 44
83 47
83 57
83 59
83 73
83 75
83 76
83 80
83 90
83 94
84 0
84 6
84 7
84 11
84 15
84 23
84 46
84 58
84 63
84 67
84 76
84 89
84 95
84 96
85 3
85 6
85 24
85 35
85 57
85 73
85 89
85 90
85 98
86 8
86 9
86 11

22. 86 16
86 23
86 46
86 48
86 49
86 51
86 56
86 60
86 63
86 69
86 84
86 86
86 97
87 0
87 5
87 15
87 25
87 30
87 37
87 39
87 50
87 54
87 63
87 64
87 75
87 92
88 19
88 21
88 31
88 36
88 40
88 54
88 87
88 88
88 91
88 93
89 16
89 17
89 23
89 25
89 26
89 30

23. 89 36
89 48
89 59
89 92
90 9
90 17
90 41
90 42
90 48
90 53
90 62
90 79
91 0
91 11
91 12
91 14
91 19
91 22
91 25
91 30
91 38
91 69
91 76
91 83
91 96
92 21
92 24
92 33
92 34
92 40
92 41
92 42
92 57
92 64
92 70
92 88
92 94
92 98
93 9
93 10
93 23
93 25

24. 93 53
93 65
93 69
93 87
93 89
94 11
94 26
94 37
94 51
94 65
94 74
95 3
95 9
95 25
95 28
95 58
95 59
95 71
95 81
95 85
95 91
96 7
96 30
96 39
96 49
96 55
96 57
96 58
97 0
97 5
97 18
97 20
97 49
97 50
97 57
97 67
97 68
97 69
97 70
97 84
97 92
97 95

25. 97 99
98 1
98 13
98 17
98 19
98 28
98 32
98 35
98 80
98 95
99 1
99 8
99 22
99 24
99 36
99 41
99 60
99 61
99 62
99 77
99 81
99 85
4/6 puntos (calificado) Download the file directed_graph.txt. You may use any computational tool
for this problem. The file is in the edge list format with each line " ij " indicating a directed edge
from vertex i to vertex j. For example, the edge list of the graph G=({0,1,2},{{0,1},{0,2}}) is 01 02
The example above assumes an undirected graph, but the same edge list can represent the
directed graph G=({0,1,2},{(0,1),(0,2)}) Answer the following questions.5. This graph was
generated using the following model: We fixed the number of nodes and every possible directed
edge was selected with a probability p independently of all other edges. Note that in the graph we
also consider possible edges that construct self loops. What is the maximum likelihood estimate of
p ? Provide an answer accurate to at least five significant figures (graded to 0.01% tolerance), you
can also enter your answer as an exact fraction. 6. Given the above generative model, what is the
p-value of observing this graph for the null hypothesis that p=0.1 ? Assume that the test statistic is
nSnn, where Sn is the sample mean and n and n are the mean and standard deviation of the
sample mean under the null hypothesis. The sample mean is the fraction of number of edges
observed to the total number of possible edges. Use the central limit theorem approximation to
compute the required probability. Provide an answer accurate to at least three significant figures
(graded to 1% tolerance).