Basics

Question 1

(D) p-th moment, q-th centered moment

Answer 1

1. p-th moment: E[|X|^p]

2. q-th centered moment: E[|X - µ|^q]

Question 2

“Wall against ground”

Answer 2

Falls in Aufgabenstellung auftaucht: “plot a against b”, dann gehört a auf die y-Achse und b auf die x-Achse.

Question 3

rep(1,5)

Answer 3

1, 1, 1, 1, 1

Question 4

1:4

Answer 4

1, 2, 3, 4

Question 5

seq(1,25,4)

Answer 5

1, 5, 9, 13, 17, 21, 25

Question 6

v=c(1,2,3)

Answer 6

combine 1, 2, 3 into a vector v

Question 7

v[i]

Answer 7

i-tes Element von v

Question 8

length(v)

Answer 8

Länge von v

Question 9

sort(v)

Answer 9

Einträge von v sortieren

Question 10

sapply(v,f)

Answer 10

wende Funktion f auf alle Einträge von v an

Question 11

cbind(v,w), rbind(v,w)

Answer 11

kombiniere v, w zu einer Matrix

Question 12

matrix(v,3,5)

Answer 12

Matrix von v mit 3 Reihen und 5 Spalten

Question 13

M %*% N

Answer 13

Matrizenprodukt M*N

Question 14

t(M)

Answer 14

M transponiert

Question 15

det(M)

Answer 15

Determinante von M

Question 16

solve(M), solve(M,b)

Answer 16

Inverse von M, Lösung von Mx=b

Question 17

eigen(M)

Answer 17

Eigenwerte und Eigenvektoren von M

Question 18

apply(M,i,f)

Answer 18

wende f auf die Reihen (i=1) oder Spalten (i=2) der Matrix M an

Question 19

write(v,“file.dat”)

Answer 19

schreibe Vektor v in die Datei “file.dat”

Question 20

scan(“file.dat”)

Answer 20

lese die Datei “file.dat” und speichere als Vektor

Question 21

write.table(t,“table.table”)

Answer 21

speichere die Tabelle t in die Datei “table.table”

Question 22

read.table(“table.table”)

Answer 22

lese die Datei “table.table” und speichere als Vektor

Question 23

sum(v), prod(v)

Answer 23

Summe/Produkt der Einträge

Question 24

cumsum(v), cumprod(v)

Answer 24

kummulative Summe/Produkt der Einträge

Question 25

table(v)

Answer 25

absolute Häufigkeiten

Question 26

mean(v)

Answer 26

arithmetisches Mittel

Question 27

median(v)

Answer 27

Median

Question 28

ecdf(v)

Answer 28

empirische kumulative Verteilungsfunktion von v

Question 29

quantile(v, p)

Answer 29

empirical p quantile of v (smallest using type=1)

Question 30

min(v), max(v)

Answer 30

minimum, maximum of v

Question 31

var(v), sd(v)

Answer 31

empirical variance, standard deviation of v

Question 32

summary(v)

Answer 32

important parameters of v

Question 33

cov(v, w), cor(v, w)

Answer 33

covariance, correlation coefficient of v,w

Question 34

lm

Answer 34

linear model (see also summary, predict)

Question 35

nlm, nls

Answer 35

non-linear minimisation and least squares

Question 36

sample

Answer 36

drawing with or without replacement

Question 37

data

Answer 37

shows data sets in R

Question 38

boxplot(v)

Answer 38

box plot of v

Question 39

barplot(table(v)

Answer 39

bar plot of v

Question 40

hist(v)

Answer 40

histogram of v

Question 41

plot.ecdf(v)

Answer 41

empirical cumulative distribution function of v

Question 42

qqnorm(v)

Answer 42

qq plot v against normal distribution, compare qqPlot() in package car

Question 43

abline(a,b)

Answer 43

add line a+bx to existing graphics

Question 44

plot(v, w)

Answer 44

scatter plot w against v

Question 45

qqplot(v, w)

Answer 45

qq plot w against v

Question 46

pairs(M)

Answer 46

mutual scatter plots of the columns of M

Question 47

plot(sin)

Answer 47

graph of sin

Question 48

curve(cos(x), add=TRUE)

Answer 48

add cos to existing plot

Question 49

par(mfrow=c(3,2))

Answer 49

3×2 plots in graphics window

Question 50

t.test, binom.test, chisq.test, shapiro.test, ks.test, lillie.test, runs.test, var.test

Answer 50

``` t test, power using power.t.test binomial test chi-square test Shapiro-Wilk test Kolmogorov-Smirnov test Lilliefors test, package nortest runs test using normal approximation, package tseries test of variance ```

Question 51

xnorm, etc

Answer 51

The first letter x can take values d,p,q,r: density, probability (i.e., cdf), quantile, random number.