A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.68 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. r 0 1 2 3 4 or more O 19 22 17 18 14 (a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below. P(r) = e−λ λr r! Here λ = 1.68 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.) P(0) = P(1) = P(2) = P(3) = P(4 or more) = (b) Compute the expected number of accidents E = 90P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.) E(0) = E(1) = E(2) = E(3) = E(4 or more) = (c) Compute the sample statistic Χ2 = Σ((O – E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) df = Χ2 =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.68 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information.

r	0	1	2	3	4 or more
O	19	22	17	18	14

(a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below.

P(r) =

e^−λ λ^r

Here λ = 1.68 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.)

P(0) =
P(1) =
P(2) =
P(3) =
P(4 or more) =

(b) Compute the expected number of accidents E = 90P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.)

E(0) =
E(1) =
E(2) =
E(3) =
E(4 or more) =

(c) Compute the sample statistic Χ² = Σ((O – E)²/E) and the degrees of freedom. (Round your sample statistic to three decimal places.)

df =
Χ² =

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