#OK to post homework
#George Spahn, 2/21/2021, Assignment 9

#SAc(f,x,K): The SA(X,x,K) of the rv X such whose Pgf is f of x
SAc:=proc(f,x,K) local mu,f1,sig2,L,i:
if subs(x=1,f)=0 then
 RETURN(0):
fi:

mu:=subs(x=1,diff(f,x)):

if K=1 then
 RETURN([mu]):
fi:

f1:=f/x^mu:
f1:=x*diff(f1,x):
f1:=x*diff(f1,x):

sig2:=subs(x=1,f1):
L := [mu,sig2]:
if K=2 then
 RETURN(L):
fi:
for i from 3 to K do
 f1:=x*diff(f1,x):
 L:=[op(L),subs(x=1,f1)/sig2^(i/2)]:
od:
L:
end:

#Here are the moments for #2
# n/2, n/4, 0, 16*(3/16*n^2 - 1/8*n)/n^2, 0, 
# 64*(1/4*n - 15/32*n^2 + 15/64*n^3)/n^3, 0, 
# 256*(-17/16*n + 147/64*n^2 - 105/64*n^3 + 105/256*n^4)/n^4, 0, 
# 1024*(31/4*n + 945/1024*n^5 + 4095/256*n^3 - 1575/256*n^4 - 1185/64*n^2)/n^5

#For #3, n=100
# I got average of 28.58560000 parts with variance 5.648272640