# Aufgabe 17

# Daten
faithful
?faithful
dim(faithful)
summary(faithful$eruptions)
table(faithful$waiting)

# Parameter xlim, ylim für Funktion plot
xdim = c(40,100)
ydim = c(0,.05)

# a) Histogramm und Kerndichteschätzer
# par(mfrow = c(2,2))
hist(faithful$waiting, freq = FALSE, ylim = ydim, xlim = xdim, 
     main = "Histogramm: Standardeinstellung", xlab = "waiting")

hist(faithful$waiting, freq = FALSE, ylim = ydim, 
     xlim = xdim, 
     main = "Histogramm: 'breaks = 20'", 
     xlab = "waiting", breaks = 20)


plot(density(faithful$waiting), ylim = ydim, xlim = xdim, 
     main = "Kerndichtschätzung: Standardbandweite")
plot(density(faithful$waiting, adjust = 0.5), ylim = ydim, xlim = xdim, 
     main = "Kerndichtsch?tzung: 'adjust = 0.5'")
# (Parameter adjust = '0.5' bei Dichteschätzung war gesucht)
?density

# b)

#  QQPlot - Variable waiting vs. Normalverteilung
qqplot(y = scale(faithful$waiting), x = rnorm(1000,0,1), xlim=c(-3,3), ylim=c(-3,3),
       xlab = "theoretische Quantile", ylab = "Quantile waiting", main = "Normal-Q-Q-Plot")
abline(a = 0, b = 1)