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

# Please Edit this .txt page with Answers

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


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 6

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

QUESTION #1:

Why are Republicans red and Democrates blue?

ANSWER:

These colors started to be applied during the 2000 US presidential election. Before 2000, Democrats could be represented by red and Republicans by blue, but in 2000, major media companies began conforming to a single color-coding scheme which was coined by Tim Russert during his television program.

QUESTION #2:

In the 2008 election, in how many ways could the winner have gotten the exact number of electoral votes that he actually got.

ANSWER:

Barak Obama won in 2008 and received 365 electoral votes.
According to generating function GFv(USEC(),x), the number of ways Obama could have gotten 365 votes is the coeff of x^365 which is:
318241652483.

QUESTION #3:

What is the probability that a random count is consistent in such an election with 1000 states?

ANSWER:

If we have 1000 states contribute a vote each, then by our theorem the probability of a random count being consistent is binomial(1000,500)/2^1000 = 0.02522501818.

QUESTION #4:

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

ANSWER:

There are binomial(1000, 500) ways of getting exactly 500 0s and 500 1s. The probability is binomial(1000, 500)/2^1000 which is also the probability of a random count being consistent. We calculated this value to be binomial(1000,500)/2^1000 = 0.02522501818.

QUESTION #5:

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

The value of SimuCount([1$100],1/2,10000,4)[2]; is 0.07958923739.
The value of C(100) is 0.07958923739.

QUESTION #6:

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

ANSWER:

(i) Other countries with electoral colleges, according to Wikipedia, are Burundi, Estonia, India, Kazakhstan, Madagascar, Myanmar, Pakistan, Trinidad and Tobago[12] and Vanuatu
(ii) The counterpart of USEC for India is [7,8,8,9,16,17,18,20,26,51,58,64,72,112,116,116,129,131,131,132,147,149,151,152,159,173,175,176,176,208]