new_contents: '''
  For Homework 02, Exercieses 01-02. EdX Learning From Data course.
  Jonathan Miller
  '''
  
  import random
  
  # FUNCTIONS ###########################
  
  def runTrial(numCoins, numFlips):
  
      def flipCoin():
          if random.random() > 0.5:
              return head
          else:
              return tail
  
  
      def findv1(vList):
          return vList[0]
  
      def findvrand(vList):
          return random.choice(vList)
  
      def findvmin(vList):
          vmin = 1.
          for v in vList:
              if v < vmin:
                  vmin = v
          return vmin
  
  
      def sequencesToRatios(flipSequences):
          v1 = 0
          vrand = 0
          vmin =  0
          vList = []
  
          for sequence in flipSequences:
              numHeads = 0
              #print sequence
              for flip in sequence:
                  if flip == head:
                      numHeads += 1.
              vList.append( numHeads / numFlips)
          #print vList
          v1 = findv1(vList)
          vrand = findvrand(vList)
          vmin = findvmin(vList)
  
          return v1, vrand, vmin
  
  
      flipSequences = []
      v1 = 0
      vrand = 0
      vmin = 0
      for coin in range(numCoins):
          coinFlipResults = ""
          for flip in range(numFlips):
              coinFlipResults += flipCoin()
          flipSequences.append(coinFlipResults)
  
      v1, vrand, vmin = sequencesToRatios(flipSequences)
  
      return v1, vrand, vmin
  
  
  # MAIN ###########################
  
  
  
  numTrials = 100000
  #numTrials = 1
  numCoins = 1000
  numFlips = 10
  
  v1Exp = 0
  vrandExp = 0
  vminExp = 0
  
  head = "H"
  tail = 't'
  
  for trial in range(numTrials):
      v1Trial, vrandTrial, vminTrial = runTrial(numCoins,numFlips)
      #print v1Trial, vrandTrial, vminTrial
      v1Exp += v1Trial
      vrandExp += vrandTrial
      vminExp += vminTrial
  
  v1Exp /= numTrials
  vrandExp /= numTrials
  vminExp /= numTrials    
  
  print v1Exp, vrandExp, vminExp
  
subject: Add coin flip simulator (hw02)