R_Blatt02

#Aufgabe 1 ----
#(a)----
N <- 42
v1 <- 0:N
r1 <- 0.5^v1
r2 <- 2*(1-1/(2^(v1+1)))

#(b)----
n <- 42
p <- 1/2

W <- function(nIn,pIn,i){
  return(choose(nIn,i)*pIn^i*(1-pIn)^(nIn-i))
}

P <- function(nIn,pIn,i){
  return(sum(W(n,p,0:i)))
}

vW <- W(n,p,0:n)
vP <- cumsum(W(n,p,0:n)) #Vektor der P_i Werte
#folgende ignorieren:
vW1 <- dbinom(0:n,n,p)
vP1 <- pbinom(0:n,n,p)
#Aufgabe 2 ----
x <- c(0.61,  0.79,  0.83,  0.66,  0.94,  0.78,  0.81,  0.60,  0.88,  0.90,  0.75,  0.86,  0.74,  0.84)
y <- c(1.01,  0.13,  1.73,  0.67,  0.56,  0.99,  0.49,  0.72,  0.13,  0.48,  0.98,  0.08,  1.23 , 0.87)
x_order=order(x) # (a)----
paste("x(",1:14,":14) = ",x[order(x)],sep="") # (b)----
y_coorder <- y[x_order] # (c)----
paste("(x(",1:14,":14), y[",1:14,":14) = (",x[order(x)],",",y[order(x)],")",sep="") #(d)----
paste("(x(",format(1:14,justify="right"),":14), y[",format(1:14,justify="right"),":14) = (",format(x[order(x)],digits = 2),",",format(y[order(x)],digits=2),")",sep="") #(e)----


#Aufgabe 3----
eruptions <- faithful$eruptions
wait <- faithful$waiting
sd(wait)#(a)----
mean(wait)
max(wait)
min(wait)
(1:length(wait))[wait==max(wait)]#(b)----
(1:length(wait))[(wait==min(wait))]
quantile(wait,probs=0.3)#(c)----
wait[wait<= 60]#(d)----
length(wait)#(e)----
length(wait[wait<=60])
eruptions[wait<=60]#(f)----
mean(wait[wait<=60])#(g)----
mean(eruptions[wait<=60])
sum(eruptions[wait<=60]>=2.5)#(h)----
plot(wait,eruptions)#(i)----