# R_Blatt02

Apr 20th, 2021
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1. #Aufgabe 1 ----
2. #(a)----
3. N <- 42
4. v1 <- 0:N
5. r1 <- 0.5^v1
6. r2 <- 2*(1-1/(2^(v1+1)))
7.
8. #(b)----
9. n <- 42
10. p <- 1/2
11.
12. W <- function(nIn,pIn,i){
13.   return(choose(nIn,i)*pIn^i*(1-pIn)^(nIn-i))
14. }
15.
16. P <- function(nIn,pIn,i){
17.   return(sum(W(n,p,0:i)))
18. }
19.
20. vW <- W(n,p,0:n)
21. vP <- cumsum(W(n,p,0:n)) #Vektor der P_i Werte
22. #folgende ignorieren:
23. vW1 <- dbinom(0:n,n,p)
24. vP1 <- pbinom(0:n,n,p)
25. #Aufgabe 2 ----
26. 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)
27. 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)
28. x_order=order(x) # (a)----
29. paste("x(",1:14,":14) = ",x[order(x)],sep="") # (b)----
30. y_coorder <- y[x_order] # (c)----
31. paste("(x(",1:14,":14), y[",1:14,":14) = (",x[order(x)],",",y[order(x)],")",sep="") #(d)----
32. 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)----
33.
34.
35. #Aufgabe 3----
36. eruptions <- faithful\$eruptions
37. wait <- faithful\$waiting
38. sd(wait)#(a)----
39. mean(wait)
40. max(wait)
41. min(wait)
42. (1:length(wait))[wait==max(wait)]#(b)----
43. (1:length(wait))[(wait==min(wait))]
44. quantile(wait,probs=0.3)#(c)----
45. wait[wait<= 60]#(d)----
46. length(wait)#(e)----
47. length(wait[wait<=60])
48. eruptions[wait<=60]#(f)----
49. mean(wait[wait<=60])#(g)----
50. mean(eruptions[wait<=60])
51. sum(eruptions[wait<=60]>=2.5)#(h)----
52. plot(wait,eruptions)#(i)----
53.
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