#######################
# ---- Aufgabe 2 ---- #
#######################

# a)

	# P( Tram erwischt )
	p1 = pnorm(15, mean = 14, sd = 2)

	# P( Tram kommt rechtzeitig )
	p2 = pnorm(30, mean = 28, sd = 4)

	# P( zu spaet) = 1 - P( ings. rechtzeitig )
	pa = 1 - p1*p2
	1-p1 + p1*(1-p2)

# b)
	pp = 1 - pnorm(30,27,3)
	
# c)
	pa*pp
	
#######################
# ---- Aufgabe 4 ---- #
#######################
	CARS <- read.table("http://rosuda.org/lehre/SS10-f/STLA/datasets/Cars.txt",header=T,sep="\t",quote="")
	attach(CARS)
# a)
	hist(DealerCost, breaks = seq(0,180000,1000),freq=F, col ="grey")

# b)
	curve(dnorm(x, mean = mean(DealerCost), sd = sd(DealerCost)),add=T)

# c)
	curve(dlnorm(x, mean = mean(log(DealerCost)), sd = sd(log(DealerCost))),add=T, col = 2, lwd = 2)

# d) 
	sh = (mean(DealerCost)/sd(DealerCost))^2
	rt = mean(DealerCost)/sd(DealerCost)/sd(DealerCost)
	curve(dgamma(x, shape = sh, rate = rt),add=T, col = 4, lwd = 2, lty ="dashed")


#######################
# ---- Aufgabe R ---- #
#######################

# a)
	pnorm(20, 10, 5) - pnorm(10, 10, 5)

# b)
	sp = runif(1000)

# c)
	qn = qnorm(sp, mean = 5, sd = 2)
	hist(qn)