1. NuKcomp(50, 70)[50] = 0

2.

3.
EstimateCutOff:=proc(n,M) local i,j,max,ans:
  max:=binomial(n,2):
  for i from 1 to max do:
    ans:=0:
    for j from 1 to M do
      ans:=ans + nops(CCs(RandGr(n,i))):
    od:
    if evalf(ans/1000) < 1.05 then
       i:
       break:
    end if:
  od:
end:

EstimateCutOff(30,1000) = 83
FindCutOff(30,1.05) = 84
off by 1


4.
evalf(FindCutOff(20,1.05)/20)=2.450000000
evalf(FindCutOff(30,1.05)/30)=2.800000000
evalf(FindCutOff(40,1.05)/40)=3.
evalf(FindCutOff(50,1.05)/50)=3.160000000
evalf(FindCutOff(60,1.05)/60)=3.300000000
increases by about .2 every 10 increment


5.

EstProbKcomps:=proc(n,m,k,N) local i,co, G:

co:=0:

for i from 1 to N do

G:=RandGr(n,m):

if nops(CCs(G))=k then
 co:=co+1:
fi:

od:

evalf(co/N):
end:

6.

ProbKcomponents:=proc(n,m,k) local a,egf:
  a:=a^m:
  egf:=(log(Sum((1+a)^(n*(n-1)/2)*x^n/n!,n=0..infinity)))^k/k!:
  egf:
end: