Homeworks at
VAPMS Selected Applications of Mathematical Statistics, summer semester 2018/2019.
Homework 9 (2 points)
Compute the weighted population density of Czech Republic when it is divided to:
1. Bohemia, Moravia, and Czech Silesia.
2. 13 regions (kraje) + Prague.
(All the relevant data -- population and area -- can be found on internet).
Compare these two densities with each other and with the unweighted population
density of Czech Republic. Comment on the results.
Homework 16 (up to 2 points)
Compute correlation between two datasets of your choice. Compare the answer
with other methods of statistical comparison of two datasets we used before.
Comment on the results.
Homework 20 (up to 2 points)
This is a remake of the first question from Homework 15. Whether the identity
\(3 \times 3\) matrix
\[
\left(\begin{matrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{matrix}\right)
\]
is a correlation matrix? Note that not any symmetric matrix with units on the
main diagonal, and all elements between -1 and 1, is a correlation matrix,
so in order to answer the question you should either prove that there are 3
vectors \(\overline x, \overline y, \overline z\) such that their pairwise
correlations are zero (most probably, by explicitly constructing such vectors),
or prove that such vectors do not exist.
Homework 21 (up to 4 points)
Try to cluster your facebook friends (Homework 10) using an R function
of your choice (kmeans, hclust, etc.)
Created: Tue Oct 6 2015
Last modified: Wed Apr 15 2026 16:12:17 CEST