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.

In questions involving code which will PARTIALLY be given to you in the
question specs, you may need add new lines.  There may not be
information given as to where the lines should be inserted.

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

Do not answer any question with simulation code unless this is specified. 

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

QUESTION 

(Text answer, 25 pts.) Give the number of the "mailing tube" used to go from
(3.2) to (3.3), p.41.

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

(R code answer, 25 pts.)  Consider the bus ridership model, pp.20ff.  Find the
probability that no one alights at the second stop. 

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

(R code answer, 25 pts.)  In Sec. 2.15.3, we find the probability that two of
five winning lottery tickets are even-numbered.  Here you will solve the
problem approximately via simulation.  

simLott <- function(nreps) 
{
   countTwoEven <- 0
   for (i in 1:nreps) {
      winners <- sample(  )
      evenOdd <- winners %% 2
      twoEven <-        # boolean
      countTwoEven <- countTwoEven + twoEven
   }
   countTwoEven / nreps
}

print(simLott(5000))

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

(R code answer, 25 pts.)  Consider the Preferential Attachment Model, Sec.
2.13.1, at the time just after v4 joins the network.  Find the
probability that the degree of v1 is 1.