#Ok to post homework
#Tifany Tong, October 18th, 2020, HW #12

# Question 1

CPg := proc(L) local i, curr:
curr := CP(L[1], L[2]):
for i from 3 to nops(L) do
 curr := CP(curr, L[i]):
od:
return curr:
end:


# Question 2

AveGF := proc(f, x):
subs(x = 1, diff(f, x))/subs(x = 1, f):
end:

kthMomentGF := proc(f, x, k) local mu, f1, i:
mu := AveGF(f, x):
f1 := f/(x^mu*subs(x = 1, f)):
for i to k do
 f1 := expand(x*diff(f1, x)):
od:
subs(x = 1, f1):
end:

# Question 3

ScaledMomentGF := proc(f, x, k) local a, b, c:
a := kthMomentGF(f, x, k):
b := kthMomentGF(f, x, 2):
b := b^(k/2):
return a/b:
end:


# Question 4

# 1, 0, 3, 0, 15, 0, 105, 0, 945  --> I get A123023 in the OEIS.