#its ok to post
#TaerimKim,11/08/2020,Assignment 17a

#1. From Wiki, the results are as follows and we can get the number of ways by caculating coeff of function GFv

#year - Demo/Rep
#2000 - 267/271
#2004 - 252/286
#2008 - 365/171
#2012 - 332/206
#2016 - 227/311

#from the given data,
seq(coeff(GFv(USEC(),x),x,i),i=271,286,365,332,311); #doesnot work...
#gotta do one by one then....

#year - coeff(GFv(USEC(),x),x,i)
#2000 - coeff(GFv(USEC(),x),x,271) = 16965465344318
#2004 - coeff(GFv(USEC(),x),x,286) = 16196017263096
#2008 - coeff(GFv(USEC(),x),x,365) = 3182416524832
#2012 - coeff(GFv(USEC(),x),x,332) = 8628577597686
#2016 - coeff(GFv(USEC(),x),x,331) = 12669341528675

###########################################################################

#2. 

#2000
p := 47.9 / (47.9 + 48.4):
f := GFvp(USEC(),p,x):

#i
add(coeff(f,x,i), i = 270..538);
.4854668622

#ii
add(coeff(f,x,i), i = 271..538);
.4779353432


#2004:
p := 50.7 / (50.7 + 48.3):
#f := GFvp(USEC(),p,x):

#i
add(coeff(f,x,i), i = 270..538);
.5464029380

#ii
add(coeff(f,x,i), i = 286..538);
.4261964827


#2008:
p := 52.9 / (52.9 + 45.7):
f := GFvp(USEC(),p,x):

#i)
add(coeff(f,x,i), i = 270..538);
.6445533538

#ii)
add(coeff(f,x,i), i = 365..538);
0.6752534480e-1


#2012:
p := 47.9 / (47.9 + 48.4):
#f := GFvp(USEC(),p,x):

#i
add(coeff(f,x,i), i = 270..538);
.5780307625

#ii
add(coeff(f,x,i), i = 332..538);
.1599131129


#2016:
p := 46.1 / (46.1 + 48.1):
f := GFvp(USEC(),p,x):

#i
add(coeff(f,x,i), i = 270..538);
.4523116129

#ii
add(coeff(f,x,i), i = 304..538);
.2213345529

###################################################################################

#3. Using procedure SimCount(L,p,N,K) with N=2000, K=4, four times and with p=3/10, 2/5,1/2,3/5,7/10, and L=USEC();
#So 
L:=USEC():

# p =3/10
seq(SimuCount(L,3/10,2000,4),n=1..4);
[162.0740000, 47.24771448, .3352394428, 2.930481450], .4300000000, 
[161.4625000, 46.96806995, .2351930912, 2.772780351], .4240000000, 
[161.0045000, 46.76513103, .3038229920, 2.843617488], .4180000000, 
[160.6670000, 45.44018168, .2589458405, 2.875651401], .4210000000

StatAnal(GFvp(USEC(),3/10,x),x,4);
[807/5, (1/10)*217686^(1/2), (46552/80590467)*217686^(1/2), 1604715262/564133269]

# p= 2/5
seq(SimuCount(L,2/5,2000,4),n=1..4);
[214.7310000, 49.52548474, .2184606358, 2.924279368], .2375000000, 
[214.4285000, 49.71080252, 0.6010108177e-1, 2.789756589], .2590000000, 
[216.1240000, 50.92965368, .1535181817, 2.807734822], .2550000000, 
[214.1415000, 50.88379387, .1641630978, 2.775107460], .2490000000

StatAnal(GFvp(USEC(),2/5,x),x,4); 
[1076/5, (2/5)*15549^(1/2), (81466/80590467)*15549^(1/2), 892890989/322361868]


#p = 1/2
seq(SimuCount(L,1/2,2000,4),n=1..4);
[267.6915000, 49.30455687, -0.3099552645e-1, 2.724897676], .1525000000, 
[269.7650000, 50.77817225, -0.1064401250e-1, 2.809330356], .1565000000, 
[268.5570000, 50.31930793, -0.3741041878e-1, 2.727156310], .1570000000, 
[268.3835000, 50.97363464, 0.2399299140e-1, 2.817444842], .1605000000

StatAnal(GFvp(USEC(),1/2,x),x,4); 
[269, (1/2)*10366^(1/2), 0, 73845502/26863489]

#p = 3/5
seq(SimuCount(L,3/5,2000,4),n=1..4);
[323.5110000, 49.41942816, -.1270898286, 2.777088314], .2280000000, 
[324.3990000, 49.56838508, -.1490952392, 2.946912493], .2375000000, 
[322.6795000, 50.95220095, -.1284334715, 2.710819590], .2500000000, 
[323.8345000, 49.93460834, -.1544242879, 2.728145633], .2595000000

StatAnal(GFvp(USEC(),3/5,x),x,4); 
[1614/5, (2/5)*15549^(1/2), -(81466/80590467)*15549^(1/2), 892890989/322361868]

#p = 7/10
seq(SimuCount(L,7/10,2000,4),n=1..4);
[376.8010000, 45.57579839, -0.2566308035, 2.928799383], 0.4095000000, 
[377.8260000, 45.54809242, -0.1821061027, 2.661227570], 0.4295000000, 
[377.6275000, 47.07132612, -0.2790095277, 2.873433327], 0.4290000000, 
[377.0820000, 46.76578104, -0.3120082264, 2.855427241], 0.4255000000

StatAnal(GFvp(USEC(),7/10,x),x,4) ;
[1883/5, sqrt(217686)/10, -(46552*sqrt(217686))/80590467, 1604715262/564133269]

#All of these are very much close to each other and correspond with StatAnal