DESCRIPTION

Please keep in mind the OMSI rules.

Save your files often.

Submit each answer individually and make sure you receive the notification of successful submission.

Don't wait till the last moment to submit all answers, as there might be
network traffic in the last 5 minutes causing unexpected delay and
failure.  

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 to add new lines.  There may not be
information given as to where the lines should be inserted. 

MAKE SURE TO RUN THE R CODE ANSWER IN PROBLEMS THAT INVOLVE R CODE!


QUESTION 

(text answer - 10 pts) In our discussion of model forming in class in
connection to the library examples (one simple, one less so), a specific
application area was mentioned.  What was it?

QUESTION 

(text answer - 10 pts) In each of the applications below, state whether the
mean or median is a better measure, according to our class discussion:

   i.  Snowfall in Lake Tahoe on all January 1 days (over all years).

   ii.  The number of steps students take in traveling from Kemper Hall
   to the MU.

   iii.  Weights of a group of people entering an elevator.

Write your answers in sequence separated by comma, 
e.g. a random answer would look like "mean, median, mean"


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

(R code answer - 10 pts) If two independent random variables X and Y,
have expectation p and q respectively and variance r and s respectively.
Write a function vary(p,q,r,s) to compute Var( X/2 + Y) and print
vary(1,2,2,4.3)

vary <- function(p,q,r,s){
  out <-  # fill in the blank
}
print(vary(1,2,2,4.3))

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

(R code answer - 10 pts) The third moment of a random variable X is defined
to be E(X^3).  Find the third moment of the number of dots showing in
the single roll of a die.


QUESTION  -ext .R -run 'Rscript ./omsi_answer5.R'

(R code answer - 10 pts) In the second library model, Sec. 3.9.2, find Var(B).

QUESTION 

(text answer - 10 pts) Let X and Y be two indicator random variables.
Write true or false for each of the statements below:

(i)   if E(XY) = 0 then E(X+Y) is less than or equal to 1
(ii)  if E(X+Y) is less than or equal to 1 then  E(XY) = 0


QUESTION

(text answer - 10 pts) Consider the bus example, Sec 2.11.  Let O_i denote
the  number getting off bus at stop i, with  O_1 = 0.  Let
T_k = O_1+...+O_k.  Which one(s) of these are true?

   (i) ET_k = EO_1+...+EO_k
   (ii) Var(T_k) = Var(O_1)+...+Var(O_k)
   (iii) EO_i has the same value for all i
   (iv) EO_i = 0.2 EL_{i-1}
   (v) none of the above is true


QUESTION -ext .R -run 'Rscript ./omsi_answer8.R'

(R code answer - 10 pts) I and J are two indicator random variables.
If E(I+J) = 1.1 and E((I-J)^2) = 0.7, what is Var(IJ)?


QUESTION -ext .R -run 'Rscript ./omsi_answer9.R'

(R code answer - 10 pts) Consider the board game, Sec. 2.10.  Write a
simulation code to find ET, where T is the number of turns it takes to
reach or pass 0.

Note: bonus turns (if any) don't count as extra turns

et <- function(nreps) 
{

}

set.seed(9999);
print(et(10000))

10.  (canceled)