Question

3) A traffic engineer has observed the traffic at a certain intersection between 5 pm and 5:05 pm each day for 100 days. She has tabulated the frequency of the number of cars observed crossing the intersection during this period Number of Number Proportion Cars of Days of Days 36 28 15 10 0.36 0.28 0.15 0.10 0.07 0.04 2 P(x)(0.2)(0.8) P2(x) -(0.4)(0.6)

Answer 1

a)

number of cars,X	no. of days	proportion	p1(x) = 0.2*0.8^x
0	36	0.36	0.2
1	28	0.28	0.16
2	15	0.15	0.128
3	10	0.1	0.1024
4	7	0.07	0.08192
5	4	0.04	0.065536

b)

number of cars,X	no. of days	proportion	p1(x) = 0.2*0.8^x	p2(X)=0.4*0.6^x
0	36	0.36	0.2	0.4
1	28	0.28	0.16	0.24
2	15	0.15	0.128	0.144
3	10	0.1	0.1024	0.0864
4	7	0.07	0.08192	0.05184
5	4	0.04	0.065536	0.031104
total		1	0.737856	0.953344

c)

proportion is high from both model in(x=0,1,2)

model 2 , P2(x) seems somewhat closer to proportions,so it provide better fit than p1(x)

d)

sum of all probabilities should be 1,but here,neither model probability adds to 1.