Fundamentals of Probability and Statistics for Engineers

model 2:

where is estimated from the data;

model 3:

where k and p are estimated from the data.

(a) U se the^2 test; are these models acceptable at the 5% significance level?

(b) In you opinion, which is a better model? Explain your answer.

Note: for model 3,

10.8 Car pooling is encouraged in a city. A survey of 321 passenger vehicles coming into
the city gives the car occupancy profile shown in Table 10.10. Suggest a probabil-
istic model for X, the number of passengers per vehicle, and test your hypothesized
distribution at

Table 10.9 Arrival of cars at intersection, for Problem 10.7

Cars per interval Number of observations

0 139

1 128

255

325

4 13

n 360

Table 10.10 Car occupancy (number of passengers

per vehicle, excluding the driver), for Problem 10.8

Occupancy Vehicles (No.)

0 224

147

231

316

4 3

n 321

332 Fundamentals of Probability and Statistics for Engineers

0 05 on thebasis of this survey.

pX…x†ˆ

ex

x!

; xˆ 0 ; 1 ;...;



pX…x†ˆ

x‡k 1

k 1



pk… 1 p†x; xˆ 0 ; 1 ;...;

mXˆ

k… 1 p†

p

;

^2 Xˆ

k… 1 p†

p^2

:

ˆ :

ˆ



ˆ