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 - 20 pts) Fill in the blank:  In class, a reason was given
as to why we will be using infinite series, in settings in which we have
infinitely many ________________ events.

QUESTION

(text answer - 20 pts) Give an example of two mutually dependent events.

QUESTION

(text answer - 20 pts) Can two disjoint events with non-zero
probabilities be independent? Explain your answer.

QUESTION

(Text answer - 20 pts) "Expected value is calculated by multiplying the
mean of all values with the likelihood of all the possiblities."

True or False?

QUESTION

(text answer - 20 pts) We say the mean and median are ways to quantify
the notion of "central tendency."  What is the corresponding term for
variance?

QUESTION -ext .R -run 'Rscript ./omsi_answer6.R'

Consider the board game, Sec. 2.10, and think about P(R = 3, B <= 4).
The 2 events are NOT independent.  If we falsely compute the probability
under independence, we get the wrong answer. What is the value of the
latter?

QUESTION -ext .R -run 'Rscript ./omsi_answer7.R'

(R code answer - 20 pts) Consider the board game, Sec. 2.10, and think
about P(R = 3, B <= 4).  The 2 events are NOT independent.  If we
falsely compute the probability under independence, we get the wrong
answer.  What is the value of the latter?

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

(R code answer - 20 pts) In the board game example sec. 2.10, what is
the variance of the position after the first turn?

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

(R code answer - 20 pts) You pay $4.00 to roll a fair die anticipating
that you will win $12.00 back if you roll a 1 or a 6. Otherwise you get
$1.00 back.  What is the expected amount you win?

QUESTION -ext .R -run 'Rscript ./omsi_answer10.R'

(R code answer - 20 pts) In Problem 4, Hwk 1, we have c computers.  Time
is slotted.  Let X_i denote the number of infected computers at the
beginning of epoch i, with X_0 = 1.  Halfway through any epoch, each
infected computer may infect each of the noninfected computers. If there
are currently k infected computers, any given noninfected one will stay
noninfected with probability r^k, independently.  Write a function
nochange(c,r,k) that will find P(X_{n+1} = k | X_n = k), and print
nochange(4,0.2,3).