#Ok to post
#Michael Yen, 11/8/20, Assignment 17a
#Lecture 17a: Due Nov. 8, 9:00pm. Email ShaloshBEKhad@gmail.com an attachment

#hw17aFirstLast.txt

#Indicate whether it is OK to post

#1) Use Wikipedia (or otherwise) to find the final outcome of the electoral votes for the presidential elections for 2000, 2004, 2008, 2012, and 2016, and find the number of ways in which it could have been counted to lead to the final ouctome, by using the appropriate procedures in ComboProject8.txt.

GFv(USEC(),x)

#2000: 271-266 16965465344318
#2004: 286-251 16103591935405
#2008: 365-173 3182416524832
#2012: 332-206 8628577597686
#2016: 304-227 12669341528675

#2) Assuming, rather unrealistally, that the probability of winning for either of the candidates is the same for each state, and that they are independent of each other, use the popular vote (also given in Wikipedia), use the appropriate procedure to find the (estimated) probability of the ultimate winner of (i) winning (i.e. scoring at least 270 votes) (ii) scoring that many electoral votes or more.

#1/2

#3) Using procedure SimCount(L,p,N,K) with N=2000, K=4, four times and with p=3/10, 2/5,1/2,3/5,7/5, and L=USEC(), see whether the first component of the output (that give estimates for the expectation, standard-deviation, and the 3rd, and 4th moments) agree with each other (remember they are only statistical estimates) and how they are close to the true value obtained by using StatAnal(f,x,K) applied to GFvp(USEC(),p,x). I have no clue about the theoreical (exact) value of the probability that such a count is consistent, but the second output of SimCount(L,p,N,K) give estimates. How close, in the above-mentioned four runs are there to each other?

SimuCount(USEC(), 3/10, 2000, 4);
    #[160.4040000, 47.10677004, 0.2864513488, 2.958221627], 0.4245000000


SimuCount(USEC(), 2/5, 2000, 4);
    #[213.3075000, 49.60565435, 0.1417364603, 2.712115422],0.2430000000


SimuCount(USEC(), 1/2, 2000, 4);
    #[270.4595000, 51.66636585, -0.01873761374, 2.754023143],0.1690000000


SimuCount(USEC(), 3/5, 2000, 4);
    #[322.9630000, 49.82144750, -0.2334397982, 3.032637143],0.2360000000

#They are not that close to each other.