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 code on p.108, state the portion of
code that produces the O vector in (6.16).


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

(R code answer, 25 pts.)  Instead of the 3-Heads-in-a-Row game, say the
rule is that we must have 4 consecutive heads to win.  Then under
the approach in Sec. 6.4, the states will be 0,1,2,3.  Find p_30 (i.e.
p[4,1] in R subscript), the probability of going from state 3 to state
0.

print(              )

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

(R code answer, 25 pts.)  The code in lines 2-9, p.117, finds the
probabilities of going from state i to state j in one day.  Write code
to find the matrix for transitions occurring in two days' time.  Place
your code in a function twodays(), which returns the matrix in question.

twodays <- function(v,w,r) {



}

print(twodays(0.6,0.4,5))

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

(R code answer, 25 pts.)  Consider the 3-Heads-in-a-Row game, Sec.
6.4.  Say we record the states as the player continues playing for a
very long time.  For instance, if the player gets H,T,H,H,T,T,H,... the
record of states would be 01012001...  Find the long-run proportion of
the time the pair 12 appears, meaning we are in state 1, then
immediately afterward are in state 2.

print(              )