Answered: The number of traffic accidents on a…

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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Question

The number of traffic accidents on a section of the M4 freeway during peak flow periods
follows a Poisson distribution with a mean of 2 accidents per hour.
i. If X is the random variable representing the number of accidents in 1 hour of a peak
flow period then state the possible values of X.
ii. Determine the probability of 3 or less accidents on this section of the M4 in a randomly
selected hour during a peak flow period.
iii. Let Y be the variable representing the number of accidents across a 3-hour peak flow
period. State the type of distribution Y has and it’s parameter/s. Use these to determine
the probability of 5 accidents during a 3-hour peak flow period.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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