Fundamentals of Probability and Statistics for Engineers

282 Fundamentals of Probability and Statistics for EngineersTable 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 61–2 25 17–18 42–3 21 18–19 33–4 13 19–20 34–5 11 20–21 15–6 15 21–22 16–7 16 22–23 17–8 12 23–24 08–9 11 24–25 19–10 11 25–26 010–11 8 26–27 111–12 12 27–28 112–13 6 28–29 113–14 3 29–30 214–15 3 30–31 115–16 3Answer: in this case, 1 ˆ 1 ; ^ and, following the method of moments, the simplest estimator, ,for isobtained fromHence, the desired estimate is 1 ˆ X; or ^ ˆ 1X :…9:71†!1 X^ 214 1ˆ x j214jˆ1214ˆ18…0:5†‡25…1:5†‡‡1…30:5†ˆ 0:13 s 1 :…9:72†Let us note that, although X is an unbiased estimator for 1, theestimatorfor obtained above is not unbiased sinceE1 X6ˆ 1EfXg :TLFeBOOK