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 simplify R expressions.  If your answer is wrong but largely
corrected, the full expressions may show that you deserve partial
credit.

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, 20 points.)

Consider the Computer Worm example, pp.186ff.  This is a pure birth
process.  State the value of mu_i, i = 1,2,...,g-2.

QUESTION 

(R code answer, 20 points.)

Again consider the Computer Worm example
Find the variance of the mean time to go from state 1 to state g-1
(compute a sum, not an integral).

varTimeToAbsorb <- function(g) 
{

}

print(varTimeToAbsorb(10))


QUESTION 

(R code answer, 20 points.)

Consider the Bus Paradox, pp.188ff.  Now suppose there are two bus lines
running through that stop, A and B, and that their arrival processes are
independent of each other.  Mean time between buses on the A line is 10
minutes, and that of B is 20 minutes.  When I arrive at the bus stop, I
am curious as to the probability that the next bus arrival is from line
A, and the mean time from my arrival to the time at which any bus 
arrives.  Fill in the R code:

nextBus <- function()  
{

   c(probBusA,meanTimetoNextBus)
}

print(nextBus())


QUESTION 

(R code answer, 20 points.)

In the Machine Repair example, pp.200ff, suppose there is only one
repairperson, so if two machines are down, only one can be under repair
at a time.  Write code that computes the new Q matrix (which will still
be 3x3).

findQ <- function() 
{
   q <- matrix(0,nrow=3,ncol=3)

}

print(findQ())


QUESTION 

(R code answer, 20 points.)

In our material on length-biased sampling, pp.188ff, suppose the length
of sticks has a uniform distribution on (0,c).  Find the ratio EY/EX
(which by the way turns out to be independent of c).