#ATTENDANCE QUIZ FOR LECTURE 17a of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p17a
#with an attachment called
#p18FirstLast.txt
#(e.g. p17aDoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 6, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

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Attendance Question 1:
Why are Republicans red and Democrats blue?

The colors red and blue are featured heavily on the American flag so that's why those colors are generally used. It seems there was never an explicit agreement to use red for Republicans and blue for Democrats, but it was just gradually used by TV networks to color code their election maps and eventually the association stuck. There might be a chance that red made more sense for Republicans since they both start with R.


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Attendance Question 2:
In the 2008 election, in how many ways could Obama have gotten the exact number of electoral votes that he actually got? (Assuming the smaller candidate electoral votes contribute to Obama's).

Obama got 365 electoral votes. 
coeff(GFv(USEC(),x),x,365)
3182416524832 ways of leading to this outcome.

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Attendance Question 3:
What is the probability that it is consistent in such an election with 1000 states?

binomial(1000,500)/2^1000 = 0.2522501818e-1 is the probability such an election with 1000 states is consistent.


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Attendance Question 4:
How often will we get 500*x[0]+500*x[1]?
add(x[LC(1/2)], i = 1..1000);

binomial(1000,500) * (0.5)^1000
0.2522501817e-1 is the probability of getting exactly 500*x[0]+500*x[1].

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Attendance Question 5:

Run SimuCount([1$100],1/2,10000,4)[2];
How close is it to C(100) = 0.1591784748?

.1615000000 is the output I got. It's pretty close to C(100), differing by about 0.003. It is about 1.458% away from C(100) which is a pretty low relative error.

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Attendance Question 6:

(i) Are there other countries with the electoral college system? 
(ii) What is the counterpart of USEC() for such a country?

i) Yes. Burundi, Estonia, India, Kazakhstan, Madagascar, Myanmar, Pakistan, Trinidad and Tobago, and Vanuatu have similar electoral college systems. 
ii) For Pakistan, the net value of votes cast is split as such:
[65,65,65,65,104,342] where 104 and 342 come from the Parliament and the rest come from the various Provincial Assemblies.