#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. 7, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 7

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

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

# Answer:
# This association came about in the 2000 election. The New York Times and USA Today published full-color electoral maps. 
# According to the the senior graphics editor, red begins with 'r' and so does Republican. For blue, it was modelled
# off Great Britain's political system where its liberal party was associated with blue.
# -------------------------------------------------------------------------------------------------------------------------------
# Question 2: In the 2008 election whoever won, in how many ways could he have gotten the exact number of electoral votes that they actually got? 

# Answer:
# coeff(GFv(USEC(), x), x, 365) = 3182416524832 ways

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

# Answer:
# C := n -> evalf(binomial(n, trunc(1/2*n))/2^n)
# C(1000) = 0.02522501818

# -------------------------------------------------------------------------------------------------------------------------------
# Question 4: How often will we get 500*x[0] + 500*x[1]

# Answer: I ran add(x[LC(1/2)], i = 1 .. 1000) 50 times. I saw that I got exactly 500*x[0] + 500*x[1] two times.
# You won't often get exactly 500*x[0] + 500*x[1].  

# -------------------------------------------------------------------------------------------------------------------------------

# Question 5 Challenge: Find an Explicit Formula in p for the probability that a count of an American  election 
# wPr(a State voting for Trump) = p INDEPENDENT is consistent

# -------------------------------------------------------------------------------------------------------------------------------

# Question 6: Run SimuCount([1$100], 1/2, 10000,4). How close is this to C(100)? 

# Answer:
# SimuCount([1 $ 100], 1/2, 10000, 4)  =   [50.00820000, 5.031990934, 0.001876584845, 3.047379945], 0.1563000000
# C(100) = 0.07958923739 and 0.1563000000 are not that close.

# -------------------------------------------------------------------------------------------------------------------------------

# Question 7: Are there other countries with the electoral college system (similar to the US) Either today or
# in the past? If you find them, what is the counterpart of USEC()? 

# Answer:
# CURRENT: Germany, India, Italy, Ireland, Burundi, Estonia, Kazakhstan, Madagascar, Myanmar, Pakistan, Trinidad and Tobago, Nepal,
# Vatican City, and Vanatu

# PAST: Argentina, Paraguay, Chile, France, Spain, Taiwan, South Korea

# USEC() counterpart for Italy = [445,143,129,74,38,34,32,114]. There are 8 different general parties/groups, and the values
# in this array correspond to the number of members per party.