Fundamentals of Probability and Statistics for Engineers

(i) X 1 ,X 2 ,andX 3 are annual premiums paid by low-risk, medium-risk, and

high-risk drivers. The frequency diagram for each group is given in Figure 8.5.

(simulated results, over 50 years, are from F erreira, 1974).

(j) X is the number of blemishes in a certain type of image tube for television,

58 data points are used for construction of the histogram shown in Figure 8.6.

(source: Link, 1972).

(k) X is the difference between observed and co mputed urinary digitoxin

excretion, in micrograms per day. In a study of metabolism of digitoxin

to digoxin in patients, long-term studies of urinary digitoxin excretion were

carried out on four patients. A histogram of the difference between

Table 8.3 M aximum flood flows (in 1000 cfs), 1902–60 (source:

Benjamin and Cornell,1970).

Year Flood Year Flood Year Flood

1902 42 1922 36 1942 110

1903 102 1923 22 1943 108

1904 118 1924 42 1944 25

1905 81 1925 64 1945 60

1906 128 1926 56 1946 54

1907 230 1927 94 1947 46

1908 16 1928 185 1948 37

1909 140 1929 14 1949 17

1910 31 1930 80 1950 46

1911 75 1931 12 1951 92

1912 16 1932 23 1952 13

1913 17 1933 9 1953 59

1914 122 1934 20 1954 113

1915 81 1935 59 1955 55

1916 42 1936 85 1956 203

1917 80 1937 19 1957 83

1918 28 1938 185 1958 102

1919 66 1939 8 1959 35

1920 23 1940 152 1960 135

1921 62 1941 84

Table 8.4 Time gaps between vehicles (in seconds)

4.1 3.5 2.2 2.7 2.7 4.1 3.4 1.8 3.1 2.1

2.1 1.7 2.3 3.0 4.1 3.2 2.2 2.3 1.5 1.1

2.5 4.7 1.8 4.8 1.8 4.0 4.9 3.1 5.7 5.7

3.1 2.0 2.9 5.9 2.1 3.0 4.4 2.1 2.6 2.7

3.2 2.5 1.7 2.0 2.7 1.2 9.0 1.8 2.1 5.4

2.1 3.8 4.5 3.3 2.1 2.1 7.1 4.7 3.1 1.7

2.2 3.1 1.7 3.1 2.3 8.1 5.7 2.2 4.0 2.7

1.5 1.7 4.0 6.4 1.5 2.2 1.2 5.1 2.7 2.4

1.7 1.2 2.7 7.0 3.9 5.2 2.7 3.5 2.9 1.2

1.5 2.7 2.9 4.1 3.1 1.9 4.8 4.0 3.0 2.7

254 Fundamentals of Probability and Statistics for Engineers