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 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.

Do not answer question via simulation code unless this is specified. 

If you finish early, please leave the exam room.  If you stay, close
your laptop and sit quietly.

MAKE SURE TO RUN THE CODE IN PROBLEMS THAT INVOLVING CODE!  Hit the OMSI
Run button.

QUESTION -ext .R -run 'Rscript omsi_answer1.R'

Find the value of P(D = 3) in the parking space example, Sec. 4.2.2.

print(                             )

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

Add code to the parking space example simulation, p.74, so that the
value returned will be the approximate value of P(D = 3).  (The the call
to mean() in the book has been deleted, but you may call that function
in your own code.  You must make use of nvals or dvals or both.  For
full credit, do not use loops.)

parksim <- function(nreps) {
   nvals <- rgeom(nreps,0.15) + 1
   dvals <- ifelse(nvals <= 10,11-nvals,nvals-11)
}

print(parksim(10000))

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

Consider the committee problem, Sec. 3.9.3.  In choosing people at
random, we of course do so without replacement; we wouldn't want to
choose the same person twice.  But suppose we were to sample WITH
replacement.  What would be the value of ED now?  Hint:  This can be
done without resorting to a lot of computation.

print(             )

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

Suppose X and Y are indicator variables with P(X = 1) = P(Y = 1) = v,
and such that P(X = Y = 1) = w.  Write an R function to calculate 
Var(X + Y).  Hint:  Make use of the "mailing tubes" in Sections 3.8 and
3.9.

varxy <- function(v,w) 
{

}

print(varxy(0.5,0.2))

QUESTION -ext .R -run 'Rscript omsi_answer5.R'

Consider the Watts-Strogatz graph model, Section 3.13.3 of our book.
Fill in the details of the function below, which finds the probability
that a specified node connects to exactly one shortcut.  Here n is the
number of nodes on the circle, and s is the total number of shortcuts in
the graph.

calc1short <- function(n,s)
{
}

print(calc1short(80,20))  # about 0.31