Page 299 - Fundamentals of Probability and Statistics for Engineers

282 Fundamentals of Probability and Statistics for Engineers

Table 9.1 Observed traffic gaps on Arroyo Seco Freeway,
for Example 9.11 (Source: Gerlough, 1955)
Gap length (s) Gaps (No.) Gap length (s) Gaps (No.)

0–1 18 16–17 6
1–2 25 17–18 4
2–3 21 18–19 3
3–4 13 19–20 3
4–5 11 20–21 1
5–6 15 21–22 1
6–7 16 22–23 1
7–8 12 23–24 0
8–9 11 24–25 1
9–10 11 25–26 0
10–11 8 26–27 1
11–12 12 27–28 1
12–13 6 28–29 1
13–14 3 29–30 2
14–15 3 30–31 1
15–16 3

Answer: in this case,
1
1 ˆ ;

^
and, following the method of moments, the simplest estimator, ,for is
obtained from
^
1 ˆ X; or ˆ 1 : 9:71†
X
Hence, the desired estimate is

! 1
214
1
^
X
ˆ x j
214
jˆ1
214 9:72†
ˆ
18 0:5†‡ 25 1:5† ‡ ‡ 1 30:5†
1
ˆ 0:13 s :
Let us note that, although X is an unbiased estimator for 1 ,the estimator
for obtained above is not unbiased since
1 1

E 6ˆ :
X EfXg

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