DESCRIPTION

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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 a 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.

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SHOW YOUR WORK in problems involving numerical answers.  Either do so
via comment lines or multiline code with variable names, or in a
detailed numerical expression if it clearly shows your thinking. You
need not show ALL details, but enough to demonstrate your insight.
Single-number answers will likely get 0 credit.

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QUESTION 

In class, we discussed the fact that many R users write C/C++ code for
the crucial parts of the program for speed, with the other parts in R in
order to take advantage of R's features.  This means calling C/C++ from
R.  Which two incompatibilities were cited between R on the one hand and
C/C++ on the other hand, which must be resolved into to make this scheme
work?

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

Find the skewness of the random variable L_1 in the bus ridership model,
Sections 2.12 and 3.12.  You may use values already computed in the
book.

print(                   )

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

In the parking space example, p.73, it says that P (N = 12 | N > 10 and
N <= 16) "can be evaluated as above."  Evaluate it.

print(                    )  # about 0.205

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(rX + sY) for any constants r and s:

varrxsy <- function(v,w,r,s) 
{

}

print(varrxsy(0.4,0.3,2,-1))  # about 0.64

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

Consider the 3-heads-in-a-row game, Section 6.4, a Markov chain with
states 0, 1 and 2.  Let W_i denote the time it takes to next reach state
2, starting in state i, i = 0,1,2.  (Note the word "next"; W_2 is not
0.)  Let d_i = EW_i, i = 0,1,2.  Find the vector (d_0, d_1, d_2).

print(                       )