STATS 782
THE UNIVERSITY OF AUCKLAND
SEMESTER 2, 2018
Campus: City
STATISTICS
Statistical Computing
(Time allowed: TWO Hours)
INSTRUCTIONS
• This examination is in two parts, Part A and Part B.
• Attempt ALL questions in Part A.
• Attempt ALL questions in Part B.
• Unless asked for, avoid using explicit loops if ever possible.
• The total marks for this examination are 100 marks.
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STATS 782
PART A
1. [10 Marks] Write down the evaluation results of the following R expressions,
which are not necessarily meaningful in practice. [2 marks each]
(a) 0:1 * 1:4
(b) if ({1;2} >= 3) {4;5} else {6;7}
(c) NA | TRUE ! FALSE
(d) mean(0:9 > 7)
(e) {s = 12; while(s > 5) s = s / 2; s}
Answer:
a. 0 2 0 4
b. 7
c. TRUE
d. 0.2
e. 3
2. [6 Marks] Use :, seq(), rep() and some other commonly-used operators/-
functions, but definitely not c() or a loop, to create the sequences below. [2 marks
each]
(a) 2 4 6 8 10 12 14 16 18 20
(b) 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
(c) "a1" "b1" "c1" "a2" "b2" "c2" "a3" "b3" "c3"
Answer:
a. 1:10 * 2 # or, seq(2, 20, by=2)
b. rep(1:5, 1:5)
c. paste0(letters[1:3], rep(1:3,each=3))
3. [8 Marks] Write an R function named ldss() that finds and returns the (first)
longest decreasing subsequence of a given sequence, where decreasing does not have
to be strict. Taking the following sequence as an example,
> x = c(69, 16, 92, 83, 13, 28, 68, 37, 19, 19)
your function should perform as follows
> ldss(x) # longest decreasing subsequence
[1] 68 37 19 19
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STATS 782
Answer:
## The three lines in the function below find, respectively:
## (1) The index of the last element in each decreasing subsequence
## (2) The length of each decreasing subsequence, and then the index
## of the decreasing subsequence before the longest
## (3) The longest decreasing subsequence
ldss = function(x) {
i = c(0, which(diff(x) > 0), length(x))
im = which.max(diff(i))
x[(i[im]+1):i[im+1]]
}
4. [8 Marks] Write an R function named nnc() such that, for each of the centres
(given in an R vector center), finds and returns the number of x-values (given in
an R vector x) that are nearest to it. Taking the following data as an example,
> x = c(48, 13, 33, 31, 21, 16, 50, 17, 29, 78)
> centre = c(20, 60, 100)
your function should perform as follows
> nnc(x, centre)
centre count
[1,] 20 7
[2,] 60 3
[3,] 100 0
The result means that 7 of the 10 values in x are nearest to center at 20 (of all three
centres), 3 of them are nearest to centre at 60, and no x-value is nearest to centre
at 100. Note that vectors x and center can be arbitrarily long.
Answer:
nnc = function(x, center) {
xc = abs(outer(x, center, "-"))
i = apply(xc, 1, which.min)
cbind(center=center, count=tabulate(i, nbins=length(center)))
}