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 -ext .R -run 'Rscript omsi_answer1.R'

(Code answer.) What is the mean age in the 'pe' dataset?

load('SuppFile')
print(                     )

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

(Code answer.) Consider a random variable having a beta distribution
with both parameters being 0.2.  Find the value of the hazard function
at 0.75.

print(                      )

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

(Code answer.) Suppose in (12.4) we use 1.80 instead of 1.96, in both
instances.  What will be the new approximate confidence level, instead
of 0.95?

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

(Code answer.) In the example in Sec. 11.2.1, suppose we take a simple
random sample of size 2; note that this is WITHOUT replacement.  Find
Cov(X1,X2).  Note:  Your printed expression must show your work; do NOT
simplify.

print(               )

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

(Code answer.)  Suppose we take a random sample of size 10 from a
population in which the distribution is exponential with lambda = 1.
We use (12.4) to form a confidence interval, with approximate confidence
level 0.95. For small samples, the true level may be different.  Use
simulation to find the true level here.

Note: You probably will want to use R's mean() function, as well 
as sd() or var()). Please note that sd() and var() "divide by n-1,"
requiring an adjustment on your part.

simCI <- function(nreps) 
{

   return(trueConfLevel)
}

print(simCI(10000))