Ok to post Question 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. Answer 1 Bush won in 2000 with 271 votes - 16965465344318 ways to do it Bush won in 2004 with 286 votes- 16196017263096 ways to do it Obama won in 2008 with 365 votes - 3182416524832 ways to do it Obama won in 2012 with 332 votes - 8628577597686 ways to do it Donald Trump won 2016 with 306 votes - 13542557836144 ways to do it Question 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. Answer 2 I use the GFvp function to calculate the probability of each candidate winning accorfing to teh popular vote Winning 2000 - 0.48 2004 - 0.546 2008 - 0.64 2012 - 0.57 The actual electoral votes 2000 - 0.47 2004 - 0.42 2008 - 0.06 2012 - 0.16 Question 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? [160.6440000, 46.98660728, 0.2650279441, 2.912817952], 0.4225000000 [161.4665000, 47.00560475, 0.2383917008, 2.773060860], 0.4230000000 [160.9535000, 46.80494993, 0.3043801763, 2.837524875], 0.4190000000 [160.7020000, 45.47474240, 0.2554820887, 2.872253222], 0.4200000000 2/5 [213.9915000, 49.68485109, 0.1192262487, 2.714988077], 0.2430000000 [214.6100000, 49.47222352, 0.2193838442, 2.930825779], 0.2385000000 [214.4275000, 49.67986255, 0.06137458657, 2.794799001], 0.2580000000 [216.1210000, 50.94335441, 0.1529915299, 2.805434154], 0.2565000000 1/2 [267.9425000, 51.15010452, 0.007247263025, 2.731127553], 0.1495000000 [268.1610000, 50.94689469, -0.02783231501, 2.701742706], 0.1490000000 [269.6325000, 50.29099764, -0.007424705898, 2.788045159], 0.1575000000 [269.5290000, 49.87452414, -0.03605700034, 2.745857657], 0.1560000000 3/5 [322.5715000, 50.26003270, -0.07853819985, 2.695399749], 0.2325000000 [323.2560000, 49.48718484, -0.1271544504, 2.767762128], 0.2260000000 [324.3545000, 49.56066818, -0.1473451566, 2.948100417], 0.2375000000 [322.6850000, 50.97925828, -0.1289428368, 2.706913918], 0.2505000000 5/7 [381.6000000, 46.54162653, -0.3690886064, 2.881388827], 0.4250000000 [384.0060000, 46.45971334, -0.3409909170, 2.784941854], 0.4645000000 [384.0855000, 46.33763254, -0.2513916218, 2.871249664], 0.4425000000 [384.9580000, 46.75448894, -0.2347895966, 2.774915768], 0.4630000000 They all seem very similar.