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, 25 pts.)  In our class discussion of the "Pythagorean
Theorem" for variance, we gave an explanation for the need for the
second term in the formula.  The (hypothetical) example consists of a
situation involving finding the variance in weight among all UCD
students.  Explain.

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

(R code answer, 20 pts.)  Say X has a binomial distribution with n = 2
trials and success probability p = 0.2.  Find E(X | X <= 1).

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

(R code answer, 30 pts.)  Consider the "trick coins" example, pp.103ff
of PSB.  Let N denote the number of heads in the first two tosses.  Find
EN and Var(N).  Your code must print these two quantities as a
two-element vector, i.e. final line of code should be

print(c(eN,varN))

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

(R code answer, 25 pts.) In data from a subset of an old census, there
were six occupations.  The R vectors below give the within-occupation
wage means, wage variances and proportions of the six occupations:

means <- c(50396.47,51373.53,68797.72,53639.86,67019.26,69494.44)

vars <- c(2314077046,1822538680,2357274094,1576480779,3312502360,2732145307)

props <- c(0.22857143,0.22389248,0.33947237,0.02493778,0.03992036,0.14320557)

For example, the third occupation made up about 34% of the total rows in
the dataset, and the mean wage and variance of wage in that occupation
were 68797.72 and 2357274094, respectively.  Find and print the variance
of wage in the entire dataset.