Maximum Likelihood fitting of truncated, mixed, two populat

import math
import random

#FUNCTIONS

def getNormalizer(mu,sigma,dataRange):
#make the resolution on this large.

 n=0
 for count in range(dataRange[0]*100,dataRange[1]*100):
  #density * volume
  n+=(math.exp((-1.0/2.0)*pow(float(count)*0.01-mu,2)/pow(sigma,2)))*0.01

 return(n)



#MAIN

print "Demonstration of MLE disentangling two mixed, truncated, unnormalized Gaussians"

#DECLARE THE TRUE DATA PARAMETERS (ANSWERS)
trueSig1=0.6
trueSig2=0.8
trueMu1=3.
trueMu2=6.
trueRatio=0.3
dataSize=1000.

#This is the problem. setting both limits to [-10,20] (sampling the whole population) works brilliantly, setting it to say [1,6] and [3,10] doesn't work.
range1=[-10,20]
range2=[-10,20]




#DECLARE THE SEARCH SPACE
 #brute grid
sigma1List=[0.3,0.4,0.5,0.6,0.7,0.8,0.9]
sigma2List=[0.3,0.4,0.5,0.6,0.7,0.8,0.9]
mu1List=[1.,2.,3.,4.,5.,6.,7.,8.,9.,10.]
mu2List=[1.,2.,3.,4.,5.,6.,7.,8.,9.,10.]
ratioList=[0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]

print "Generating Data..."
#CREATE DATA ARRAY X
x=[]
#gauss1
count=0
while count < int(dataSize*trueRatio):
 guess=random.gauss(trueMu1,trueSig1)
 if guess > range1[0] and guess < range1[1]:
  x.append(guess)
  count+=1

#gauss2
count=0
while count < int(dataSize*(1.0-trueRatio)):
 guess=random.gauss(trueMu2,trueSig2)
 if guess > range2[0] and guess < range2[1]:
  x.append(guess)
  count+=1

#LOOP THROUGH PARAMETERS IN A BRUTE FORCE GRID SEARCH
maxProb=-99999999999
for mu1 in mu1List:
 print "Sanity Counter: "+str(mu1)
 for mu2 in mu2List:
  for sigma1 in sigma1List:
   for sigma2 in sigma2List:
    for ratio in ratioList:
     workingProb=0.

     n1=getNormalizer(mu1,sigma1,range1)
     n2=getNormalizer(mu2,sigma2,range2)

     for item in x:
      prob1=(ratio/n1)*math.exp((-1.0/2.0)*pow(item-mu1,2)/pow(sigma1,2))
      prob2=(((1.0-ratio)/n2))*math.exp((-1.0/2.0)*pow(item-mu2,2)/pow(sigma2,2))
      workingProb+=math.log(prob1+prob2)

     if workingProb > maxProb:
      maxProb = workingProb
      maxSigma1 = sigma1
      maxSigma2 = sigma2
      maxMu1 = mu1
      maxMu2 = mu2
      maxRatio=ratio


print "Values (true :: max)"
print "Gaussian 1: ratio ("+str(trueRatio)+":"+str(maxRatio)+") // sigma ("+str(trueSig1)+":"+str(maxSigma1)+") // mu ("+str(trueMu1)+":"+str(maxMu1)+")."
print "Gaussian 2: ratio ("+str(1.0-trueRatio)+":"+str(1.0-maxRatio)+") //sigma ("+str(trueSig2)+":"+str(maxSigma2)+") // mu ("+str(trueMu2)+":"+str(maxMu2)+")."