Random Number Generation
Since we have said that competitors' average price, quantity sold and cost behave in a random fashion but follow a normal distribution, if we want to determine the profits for different values of competitor's average price, quantity sold and cost, we must use in our trials, randomly selected numbers which follow a normal distribution. If we try to select values randomly, it may not be really random or may not follow a normal distribution and we may start repeating the numbers in a predictable pattern. For example, if a person is asked to predict the outcome of the toss of a coin in ten successive trials and he predicts it as head, head, tail, head, tail, head, head, tail, head and tail we may conclude that he would predict 2 heads, then a tail, then a head and again a tail and keep repeating this pattern. If a sure pattern could be detected, then the random characteristic is lost and any conclusion drawn from the simulation done would also be erroneous. Incidentally, when we ask a person to predict the outcome of the toss of a coin in successive trials, we adopt simulation as, without actually tossing the coin, we try to predict the outcomes.
Mathematicians have devised a variety of procedures to generate random numbers. With these procedures, random number generation can be done either manually or with the help of a computer. Also, several collections of random number tables are available. The most commonly used table contains uniformly distributed (or normally distributed) random numbers over the interval 0 to 1. To generate other types of random numbers which obey other distribution laws, we require access to a computer. A random number table is illustrated below.
Table of Random Digits
|
97
|
95
|
12
|
11
|
90
|
49
|
57
|
13
|
86
|
81
|
|
02
|
92
|
75
|
91
|
24
|
58
|
39
|
22
|
13
|
02
|
|
80
|
67
|
14
|
99
|
16
|
89
|
96
|
63
|
67
|
60
|
|
66
|
24
|
72
|
57
|
32
|
15
|
49
|
63
|
00
|
04
|
|
96
|
76
|
20
|
26
|
72
|
12
|
77
|
23
|
79
|
46
|
|
55
|
64
|
82
|
51
|
73
|
94
|
26
|
18
|
37
|
31
|
|
50
|
02
|
74
|
70
|
16
|
85
|
95
|
32
|
85
|
67
|
|
29
|
53
|
08
|
33
|
81
|
34
|
30
|
21
|
24
|
25
|
|
58
|
16
|
01
|
91
|
70
|
07
|
50
|
13
|
18
|
24
|
|
51
|
16
|
69
|
67
|
16
|
63
|
11
|
06
|
36
|
10
|
|
04
|
55
|
36
|
97
|
30
|
99
|
80
|
10
|
52
|
40
|
|
86
|
54
|
35
|
61
|
59
|
89
|
64
|
97
|
16
|
02
|
|
24
|
23
|
52
|
11
|
59
|
10
|
88
|
68
|
17
|
39
|
|
39
|
36
|
99
|
50
|
74
|
27
|
69
|
48
|
32
|
68
|
|
47
|
44
|
41
|
86
|
83
|
50
|
24
|
51
|
02
|
08
|
|
60
|
71
|
41
|
25
|
90
|
93
|
07
|
24
|
29
|
59
|
|
65
|
88
|
48
|
06
|
68
|
92
|
70
|
97
|
02
|
66
|
|
44
|
74
|
11
|
60
|
14
|
57
|
08
|
54
|
12
|
90
|
|
93
|
10
|
95
|
80
|
32
|
50
|
40
|
44
|
08
|
12
|
|
20
|
46
|
36
|
19
|
47
|
78
|
16
|
90
|
59
|
64
|
|
86
|
56
|
24
|
88
|
94
|
14
|
58
|
49
|
80
|
79
|
|
12
|
88
|
12
|
25
|
19
|
70
|
40
|
06
|
40
|
31
|
|
42
|
00
|
50
|
24
|
60
|
90
|
69
|
60
|
07
|
86
|
|
29
|
98
|
81
|
68
|
61
|
24
|
90
|
92
|
32
|
68
|
|
36
|
63
|
02
|
37
|
89
|
40
|
81
|
77
|
74
|
82
|
|
01
|
77
|
82
|
78
|
20
|
72
|
35
|
38
|
56
|
89
|
|
41
|
69
|
43
|
37
|
41
|
21
|
36
|
39
|
57
|
80
|
|
54
|
40
|
76
|
04
|
05
|
01
|
45
|
84
|
55
|
11
|
|
68
|
03
|
82
|
32
|
22
|
80
|
92
|
47
|
77
|
62
|
|
21
|
31
|
77
|
75
|
43
|
13
|
83
|
43
|
70
|
16
|
|
53
|
64
|
54
|
21
|
04
|
23
|
85
|
44
|
81
|
36
|
|
91
|
66
|
21
|
47
|
95
|
69
|
58
|
91
|
47
|
59
|
|
48
|
72
|
74
|
40
|
97
|
92
|
05
|
01
|
61
|
18
|
|
36
|
21
|
47
|
71
|
84
|
46
|
09
|
85
|
32
|
82
|
|
55
|
95
|
24
|
85
|
84
|
51
|
61
|
60
|
62
|
13
|
|
70
|
27
|
01
|
88
|
84
|
85
|
77
|
94
|
67
|
35
|
|
38
|
13
|
66
|
15
|
38
|
54
|
43
|
64
|
25
|
43
|
|
36
|
80
|
25
|
24
|
92
|
98
|
35
|
12
|
17
|
62
|
|
98
|
10
|
91
|
61
|
04
|
90
|
05
|
22
|
75
|
20
|
|
50
|
54
|
29
|
19
|
26
|
26
|
87
|
94
|
27
|
73
|
|