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'

(R code answer, 25 pts.) If the standard deviation of car speeds on a highway 
is 15.6 mph, find the variance in ft/s. (Note:  there are 5280 ft/mi.)

# you may use extra variables to show your work 
vr <-
print(vr)

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

From Homework 1: Consider a communications line in which the true bits
are 1 or 0, independently with probability of a 1 being p each. At any
given bit, the line will fail, independently with probability q. Once
the line has failed, it stays failed until it is repaired, reporting
each bit as 0 regardless of the bit's true value. 

(R code answer, 25 pts.) Find expected value of the number of bits reported 
as 0s, among the first 2 bits, with p = 0.4 and q = 0.8.

# you may use extra variables to show your work 
E_B_i12 <-
print(E_B_i12)

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

(R code answer, 25 pts.) Consider the Preferential Attachment Model in 2.13.1; 
Let D_j be the degree of v_1 just after v_j is added; find Var(D_3). 

# you may use extra variables to show your work 
Var_D3 <-
print(Var_D3)


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

(R code answer, 25 pts.) Say you roll 1 die, and let X be the number 
of dots shown; find Var(sqrt(X)). (Note: a number on p.49 will be useful.)

# use extra variables to show your work 
Var_sqrtX <- 
print(Var_sqrtX)