DESCRIPTION

Students:  Please keep in mind the OMSI rules.  Save your files often,
make sure OMSI fills your entire screen at all times, etc.  Remember
that clicking CopyQtoA will copy the entire question box to the answer
box.  

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*                                                                     *
*  Don't forget to FREQUENTLY save and submit your work, even work    *
*  in progress.  The network may get busy at the end of the exam      *
*  period, making it difficult to submit then.  The server will shut  *
*  down at the appointed time, and NO further work will be accepted.  *
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In questions involving code which will PARTIALLY be given to you in the
question specs, you need to add new lines.  There may not be information
given as to where the lines should be inserted.  Do not modify the lines
already there unless instructed to do so.

If a question includes test code, make sure to include it in your
submission.

IF YOU FINISH EARLY, please leave the exam room.  If you stay, close
your laptop and sit quietly.

QUESTION 

Consider this R session:

> head(faithful)
  eruptions waiting
1     3.600      79
2     1.800      54
3     3.333      74
4     2.283      62
5     4.533      85
6     2.883      55
> nrow(faithful); ncol(faithful)
[1] 272
[1] 2
> class(faithful)
[1] "data.frame"
> length(faithful)
[1] 2
> length(as.matrix(faithful))
[1] 544

Explain in detail the reason for the values of the two lengths.

QUESTION -ext .R -run 'Rscript omsi_answer2.R'

Write function whose arguments are a matrix m and positive integer k,
that returns a vector whose i-th element is the k-th largest value in
row i of m.  (The 1-st largest is the max, etc.)  For full credit, your
code must be loop-free.

findAllKths <- function(m,k) 
{

}

m <- matrix(c(5,8,2,6,9,12,1,4,16,1,18,5),nrow=4)
print(findAllKths(m,2)) # 9,8,2,5

QUESTION -ext .R -run 'Rscript omsi_answer3.R'

Alter the code for MachRep.R, enclosed below, so that it prints out one
additional piece of information:  The proportion of machine breakdowns
that acquire repair service immediately, rather than having to queue for
it.

DON'T FORGET TO USE AN EXPLICIT CALL TO 'print()' TO PRINT OUT THAT
PROPORTION.  

Add the following to the code:

source('DES.R')
mrp(5,1,10000,6,2)  # new output about 0.78 or 0.79

QUESTION -ext .R -run 'Rscript omsi_answer4.R'

Change the model slightly for MachRep.R, as follows:  When a repair is
complete, and no queued jobs are waiting for service, that repairperson
takes a coffee break, lasting 0.1 unit of time.  During that time, any
jobs newly joining the queue will wait.

This question is independent of Question 3.  Do NOT include your code
modifications for that question here.

Add the following to the code:

source('DES.R')
mrp(5,1,10000,4,2)