Fundamentals of Probability and Statistics for Engineers

Answer: in this case,

and, following the method of moments, the simplest estimator, ,for is
obtained from

H ence, the desired estimate is

Let us note that, althoughX is an unbiased estimator for 1 ,theestimator
for obtained above is not unbiased since

Table 9.1 Observed traffic gaps on Arroyo Seco Freeway,

for Example 9.11 (Source: G erlough, 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

282 Fundamentals of Probability and Statistics for Engineers

1 ˆ

1



;

^ 

1 ˆX; or ^ˆ

1

X

: … 9 : 71 †

^ˆ^1

214

X^214

jˆ 1

xj

! 1

ˆ

214

18 … 0 : 5 †‡ 25 … 1 : 5 †‡‡ 1 … 30 : 5 †

ˆ 0 : 13 s^1 :

… 9 : 72 †



E

1

X



6ˆ

1

EfXg

: