HW1F16sln.

(a)

> tmp = c(rep(c(3,7,6,9), 25), seq(273,0,by=-3))
> LongI = NULL
> for (i in 1:10) LongI=c(LongI, if(i %% 2 ==1) tmp else rev(tmp))

> c(minmax=range(LongI), length(LongI), freq6=sum(LongI==6))
minmax1 minmax2           freq6 
      0     273    1920     260
> LongI[100,101,192,193,194]
[1]   9 273   0   0   3


(b) 
> LongI[c(777,1000)]
[1]   3 117

### OK, since eg length(tmp) is 192, so that 4 such seq's end in position
###     4*192 = 768, and the next 9 entries are 3,6,7,9,3,6,7,9,3 the 
###     last of which is the 777'th  vector entry.


(c) 
> chstr = paste(as.character(LongI),collapse="")
> digvec = as.numeric(unlist(strsplit(chvec,sep="")))
> table(digvec)
  0   1   2   3   4   5   6   7   8   9 
160 520 440 450 190 190 440 420 160 410

> c(length(chstr), nchar(chstr))
[1]    1 3380
> length(digvec)
[1] 3380


(d) 
> tmp = sin(3*(1:120)^2 - 7)
  sumtmp = cumsum(tmp)
  inds =  pmax(1,(3-sumtmp) %/% 2)
  Dfr = data.frame(TorF = (tmp>0), Sums = sumtmp,
        Grades = c("A","B","C","D","F")[inds], 
        stringsAsFactors=F)
> Dfr = data.frame(TorF = (tmp>0), Sums = sumtmp,
        Grades = c("A","B","C","D","F")[inds])
> Dfr[1:3,]
   TorF       Sums Grades
1  TRUE  0.7568025      A
2 FALSE -0.2021218      A
3  TRUE  0.7108235      A

> sapply(Dfr,class)
       TorF        Sums      Grades 
  "logical"   "numeric" "character" 

> table(inds)
inds
 1  2  3  4  5 
24 24 33 33  6 
> sum(sumtmp <= -7)
[1] 6