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.) Jack and Jill each toss a fair coin 10 times,
resulting in X and Y heads, respectively.  Let W = X - Y. Name the parametric
distribution family, if any, that W's distribution belongs to; if none,
answer None.


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

(R code answer, 25 pts.) Consider the setting of Problem 1, but in
which each person tosses the coin n times.  Write a function g(n,k) that
finds the probability that X and Y differ by at most k. 

g <- function(n,k) 
{



}

print(g(10,3))

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

(R code answer, 25 pts.) The skewness of the distribution of a
random variable X, a measure of asymmetry, is defined to be

E[{(X - mu)/sigma}^3]

where mu and sigma are the mean and standard deviation of X, respectively.
Write a function sk(n,p) that calculates the skewness of a random
variable having a binomial distribution with parameters n and p.

sk <- function(n,p) 
{
   


}

print(sk(10,0.3))


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

(R code answer, 25 pts.) Consider the parking space example, p.76.  Let B
denote the number of the block we end up parking in.  E.g. if we park in
the second block, B = 2.  Find EB.

print(        )