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

Suppose the random variable X has density 1.5 t^0.5 on (0,1), 0
elsewhere.  Find F_X(0.5).

print(                )

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

In the parking garage example of Sec. 7.6.3.4, find P(W < 2.5).

print(                 )

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

For the random variable X in Sec. 7.4, find the skewness,
E{ [(X-mu)/sigma]^3 }, where mu and sigma are the mean and standard
deviation of X.  Feel free to use quantities already computed in the
book.

print(                )  # about -0.40

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

Consider the network buffer example, Sec. 7.6.4.2.  Suppose interarrival
times, instead of having an exponential distribution with mean 100, are
uniformly distributed between 60 and 140 milliseconds.  Write simulation
code to find the new value of (7.49).

print(                 )  # about 0.16