Riemann surface
matlab

EXERCISE 1.1 Is the upper extreme always an outlier?
EXERCISE 1.2 Is it possible for the mean or the median to lie outside of the fourths or even outside of the outside bars?

EXERCISE 1.3 Assume that the data are normally distributed $N(0,1)$. What percentage of the data do you expect to lie outside the outside bars?

EXERCISE 1.4 What percentage of the data do you expect to lie outside the outside bars if we assume that the data are normally distributed $N\left(0, \sigma^2\right)$ with unknown variance $\sigma^2$ ?

EXERCISE 1.5 How would the five-number summary of the 15 largest U.S. cities differ from that of the 50 largest U.S. cities? How would the five-number summary of 15 observations of $N(0,1)$-distributed data differ from that of 50 observations from the same distribution?
EXERCISE 1.6 Is it possible that all five numbers of the five-number summary could be equal? If so, under what conditions?

EXERCISE 1.7 Suppose we have 50 observations of $X \sim N(0,1)$ and another 50 observations of $Y \sim N(2,1)$. What would the 100 Flury faces look like if you had defined as face elements the face line and the darkness of hair? Do you expect any similar faces? How many faces do you think should look like observations of $Y$ even though they are $X$ observations?
EXERCISE 1.8 Draw a histogram for the mileage variable of the car data (Table B.3). Do the same for the three groups (U.S., Japan, Europe). Do you obtain a similar conclusion as in the parallel boxplot on Figure 1.3 for these data?

EXERCISE 1.9 Use some bandwidth selection criterion to calculate the optimally chosen bandwidth $h$ for the diagonal variable of the bank notes. Would it be better to have one bandwidth for the two groups?

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