Random number generation, Financial Management

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                                          

Posted Date: 9/15/2012 5:37:59 AM | Location : United States







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