13. For a sample of countries, the absolute frequencies for the outcomes of the variables - X=GDP per capita in 10 000 euro - Y=life expectancy at birth are provided in the following cross table Y X 10, 1] 11, 2] 12, 3] 13, 6]
13. For a sample of countries, the absolute frequencies for the outcomes of the variables - X=GDP per capita in 10 000 euro - Y=life expectancy at birth are provided in the following cross table Y X 10, 1] 11, 2] 12, 3] 13, 6]
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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could you write with a pen and paper?
![13. For a sample of countries, the absolute frequencies for the outcomes of the
variables
- X=GDP per capita in 10 000 euro
- Y=life expectancy at birth
are provided in the following cross table
Y
130, 44]
144, 58]
158, 72]
172, 86]
X
]0, 1]
16
29
52
21
11, 2]
0
1
7
22
12, 3]
0
0
0
23
13, 6]
0
0
0
9
a. Draw the histogram of Y.
b. Draw the empirical cumulative distribution function of X.
c. Determine the proportion of countries with a GDP per capita that is at most
12000 euro.
d. Calculate the quartiles of X.
e. Calculate the mean and variance of both X and Y.
f.
The covariance between X and Y is equal to 7.4122. Also determine the
correlation between X and Y. What can we learn from these values?
Extra: The calculation of the covariance is possible but quite tedious without software (e.g.
Excel). For illustrative purposes you can determine the covariance yourself, using Excel (no exam
material), applying the definition for the covariance representing each outcome by it's bin mid.
You can find the solution in countries_grouped.xlsx.
g. Determine the equation of the regression line of Y on X.
h. Compare the life expectancy in the 50% poorest countries with the life
expectancy in the 50% richest countries by drawing 2 side-by-side boxplots.
Calculate the mean life expectancy and its standard deviation for the 50%
poorest and for the 50% richest countries.
i.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F238c18ea-d48d-4177-83b5-9a3505c2d7e3%2Fccbf1dc9-6610-4443-94f5-ec24ac4e704f%2Feyp3jhm_processed.png&w=3840&q=75)
Transcribed Image Text:13. For a sample of countries, the absolute frequencies for the outcomes of the
variables
- X=GDP per capita in 10 000 euro
- Y=life expectancy at birth
are provided in the following cross table
Y
130, 44]
144, 58]
158, 72]
172, 86]
X
]0, 1]
16
29
52
21
11, 2]
0
1
7
22
12, 3]
0
0
0
23
13, 6]
0
0
0
9
a. Draw the histogram of Y.
b. Draw the empirical cumulative distribution function of X.
c. Determine the proportion of countries with a GDP per capita that is at most
12000 euro.
d. Calculate the quartiles of X.
e. Calculate the mean and variance of both X and Y.
f.
The covariance between X and Y is equal to 7.4122. Also determine the
correlation between X and Y. What can we learn from these values?
Extra: The calculation of the covariance is possible but quite tedious without software (e.g.
Excel). For illustrative purposes you can determine the covariance yourself, using Excel (no exam
material), applying the definition for the covariance representing each outcome by it's bin mid.
You can find the solution in countries_grouped.xlsx.
g. Determine the equation of the regression line of Y on X.
h. Compare the life expectancy in the 50% poorest countries with the life
expectancy in the 50% richest countries by drawing 2 side-by-side boxplots.
Calculate the mean life expectancy and its standard deviation for the 50%
poorest and for the 50% richest countries.
i.
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