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.)  In the bus problem, p.20, let N denote the
number of the stop at which we first have 2 passengers board.  What
parametric distribution family that we've studied includes the
distribution of N?  If none, answer None.

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

(R code answer, 25 pts.)  Consider the library book return example,
Version II, pp.61-62.  Find F_T(8.2361).

print(         )

QUESTION

(Text answer, 25 pts.)  Which of the follow are true, for the cdf of
any random variable X?  Answer for instance "(i) and (iii)," or "None."

(i) F_X(t) is a nondecreasing function of t.

(ii) F_X(t) has at most a finite number of breakpoints.

(iii) There must be some value of t such that F_X(t) = 1.0.

(iv) Say the support of X is (c,d), with c, d both finite. Then F_X(t)
will be 0 for all t > d.

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

(R code answer, 25 pts.)  Consider the disk drive example, pp.132-133.
Treat the requested track number as U(0,1) as in the example.  Denote the
time needed to go from the innermost track to the outermost one by fullSeek,
and the time for a full rotational delay by fullRot.  Assume the rotational
delay has the distribution U(0,fullRot).  Fill in the blanks for the
long-run average access time (seek + rotational delay; treat the actual
read/write as negligible).

sim <- function(nReqs,fullSeek,fullRot)  {
   currentTime <- 0
   currentTrackPos <- 0.5
   for (i in 1:nReqs) {
      newTrackPos <- runif(1)
      seekTime <-
      currentTime <- currentTime + seekTime
      rotDelay <-
      currentTime <- currentTime + rotDelay
      currentTrackPos <-
   }
   currentTime / nReqs
}