Answered: This cumulative review problem uses…

Name: This cumulative review problem uses material from Chapters 3, 5, and 1
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Description: This cumulative review problem uses material from Chapters 3, 5, and 10. Recall that the Poisson distribution deals with rare events. Death from the kick of a horse is a rare event, even in the Prussian army. The following data are a classic example

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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This cumulative review problem uses material from Chapters 3, 5, and 10. Recall that the Poisson distribution deals with rare events. Death from the kick of a horse is a rare event, even in the Prussian army. The following data are a classic example of a Poisson application to rare events. The data represent the number of deaths from the kick of a horse per army corps per year for 10 Prussian army corps over a period of time. Let x represent the number of deaths and f the frequency of x deaths.

x	0	1	2	3 or more
f	109	66	21	4

(a) First, we fit the data to a Poisson distribution.

The Poission distribution states

P(x) =

e^−λλ^x

where

λ ≈ x

(sample mean of x values). From our study of weighted averages, we get the following.

x =

Σxf

Σf

Verify that

x = 0.6.

Hint: For the category 3 or more, use 3.

x =

(b) Now we have

P(x) =

e^−0.6(0.6)^x

for

x = 0, 1, 2, 3 .

Find

P(0),

P(1),

P(2),

and

P(3 ≤ x).

Round to three places after the decimal.

P(0)	=
P(1)	=
P(2)	=
P(3 ≤ x)	=

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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