#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:4

#1.Why are republicans red and democrats blue?

#answer:  in the 1888 presidential election, Grover Cleveland and Benjamin Harrison used maps that coded blue for the Republicans, the color perceived to represent the Union and "Lincoln's Party", and red for the Democrats.


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#2. What is the probability that it is consisten in such an election with 10000 states?

C:=n->evalf(binomial(n,trunc(n/2))/2^n):
C(1000);
0.02522501818

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#3. How often will we get 500*x[0]+500*x[1]?

#answer: roughly i simulated 100 times

seq(add(x[LC(1/2)], i = 1 .. 1000), n = 1 .. 100);
533 x[0] + 467 x[1], 519 x[0] + 481 x[1], 499 x[0] + 501 x[1], 

  488 x[0] + 512 x[1], 506 x[0] + 494 x[1], 518 x[0] + 482 x[1], 

  475 x[0] + 525 x[1], 474 x[0] + 526 x[1], 514 x[0] + 486 x[1], 

  487 x[0] + 513 x[1], 477 x[0] + 523 x[1], 492 x[0] + 508 x[1], 

  507 x[0] + 493 x[1], 501 x[0] + 499 x[1], 527 x[0] + 473 x[1], 

  488 x[0] + 512 x[1], 479 x[0] + 521 x[1], 529 x[0] + 471 x[1], 

  493 x[0] + 507 x[1], 525 x[0] + 475 x[1], 482 x[0] + 518 x[1], 

  525 x[0] + 475 x[1], 488 x[0] + 512 x[1], 477 x[0] + 523 x[1], 

  511 x[0] + 489 x[1], 496 x[0] + 504 x[1], 519 x[0] + 481 x[1], 

  489 x[0] + 511 x[1], 526 x[0] + 474 x[1], 518 x[0] + 482 x[1], 

  506 x[0] + 494 x[1], 502 x[0] + 498 x[1], 531 x[0] + 469 x[1], 

  488 x[0] + 512 x[1], 533 x[0] + 467 x[1], 513 x[0] + 487 x[1], 

  493 x[0] + 507 x[1], 509 x[0] + 491 x[1], 489 x[0] + 511 x[1], 

  512 x[0] + 488 x[1], 493 x[0] + 507 x[1], 508 x[0] + 492 x[1], 

  515 x[0] + 485 x[1], 500 x[0] + 500 x[1], 475 x[0] + 525 x[1], 

  477 x[0] + 523 x[1], 516 x[0] + 484 x[1], 494 x[0] + 506 x[1], 

  510 x[0] + 490 x[1], 469 x[0] + 531 x[1], 509 x[0] + 491 x[1], 

  496 x[0] + 504 x[1], 461 x[0] + 539 x[1], 525 x[0] + 475 x[1], 

  503 x[0] + 497 x[1], 479 x[0] + 521 x[1], 500 x[0] + 500 x[1], 

  468 x[0] + 532 x[1], 484 x[0] + 516 x[1], 487 x[0] + 513 x[1], 

  499 x[0] + 501 x[1], 507 x[0] + 493 x[1], 505 x[0] + 495 x[1], 

  492 x[0] + 508 x[1], 519 x[0] + 481 x[1], 511 x[0] + 489 x[1], 

  504 x[0] + 496 x[1], 500 x[0] + 500 x[1], 524 x[0] + 476 x[1], 

  486 x[0] + 514 x[1], 500 x[0] + 500 x[1], 480 x[0] + 520 x[1], 

  520 x[0] + 480 x[1], 515 x[0] + 485 x[1], 507 x[0] + 493 x[1], 

  488 x[0] + 512 x[1], 507 x[0] + 493 x[1], 504 x[0] + 496 x[1], 

  463 x[0] + 537 x[1], 509 x[0] + 491 x[1], 471 x[0] + 529 x[1], 

  506 x[0] + 494 x[1], 504 x[0] + 496 x[1], 506 x[0] + 494 x[1], 

  518 x[0] + 482 x[1], 477 x[0] + 523 x[1], 510 x[0] + 490 x[1], 

  480 x[0] + 520 x[1], 479 x[0] + 521 x[1], 508 x[0] + 492 x[1], 

  522 x[0] + 478 x[1], 504 x[0] + 496 x[1], 519 x[0] + 481 x[1], 

  519 x[0] + 481 x[1], 514 x[0] + 486 x[1], 515 x[0] + 485 x[1], 

  512 x[0] + 488 x[1], 514 x[0] + 486 x[1], 505 x[0] + 495 x[1], 

  500 x[0] + 500 x[1]

#we have 5 cases out of 100 occurence. so, ill say it is roughly 0.05

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#3. run SimuCount([1$100],1/2,10000,4)[2];
#how close is it to c(100);

SimuCount([1 $ 100], 1/2, 10000, 4)[2];
                          0.1609000000
c(100);
0.07958923739

#there is a big difference between the two.

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#4. Are there any other countries with the electoral college system?
#what is the counterpart of USEC()?

#answer:
#Other countries with electoral college systems include Burundi, Estonia, India, Kazakhstan, Madagascar, Myanmar, Pakistan, Trinidad and Tobago and Vanuatu.
#For example, In Vanuatu, The counter part of USEC is fixed number with 
#52 members of Parliament and 
#1votes from each Regional Councils from 6 provinces
#3 votes from municipal councils  total 3 cities
#so counterpart of USEC()=[52,1,1,1,1,1,1,3,3,3]