By Ladislav NebeskyÌ

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**Extra resources for Algebraic properties of trees**

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10, looks almost the same from all sides, because it is a realization of random variables whose variances are equal and whose covariances are zero. The density of points corresponds to the density of a three-dimensional normal distribution which has spherical shape. Looking at the sphere from any point of view, the cloud of points always has a circular (spherical) shape. Part II Multivariate Random Variables 2 A Short Excursion into Matrix Algebra Dirty-looking rascals, but I suppose every one has some little immortal spark concealed about him.

7. Boxplots for the unemployment data. SMSboxunemp What do these graphs tell you about the data and their structure? A boxplot can be generated in the same way as in the previous examples. However, plotting a boxplot for time series data might mislead us since the distribution changes every year and the upward trend observed in this data makes the interpretation of the boxplot very diﬃcult. A histogram gives us a picture about how the distribution of the variable looks like, including its characteristics such as skewness, heavy tails, etc.

20. Rotate a three-dimensional standard normal point cloud in 3D space. Does it “almost look the same from all sides”? Can you explain why or why not? 60 Fig. 10. A 3D scatterplot of the standard normal distributed data (300 observaSMSscanorm3. tions). 10, looks almost the same from all sides, because it is a realization of random variables whose variances are equal and whose covariances are zero. The density of points corresponds to the density of a three-dimensional normal distribution which has spherical shape.

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