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Simulation Exercise Each move in the game Monopoly is determined by the total number of spots of two rolls of a die. If you play Monopoly, what should you expect to get when you roll the die two times? Question1 Represent roll result as a list of all potential spots of the die then demonstrate a roll of two dices (equivalently two times of a roll of one die) In [10]: import numpy as np In [11]: #dice array die = [1, 2, 3, 4, 5, 6] #write your code here Question 2: Simulate single move in Monoploly (it is the sum of two dices) In [12]: # one move #write your code here Question 3: Simulate all potential values of each move via 10,000 experiments. Store result into a Pandas DataFrame and display first few rows of the DataFrame In [13]: #Write your code here In [14]: #Write your code here Question 4: Plot a histogram using DataFrame function (hist() to display the distribution of the value per move in Monopoly using default bins. In [15]: #Write your code here Question 5: Plot a histogram using Matplotlib library to display the distribution of the value per move in Monopoly using default bins. In [16]: #Write your code here Question 6: Choose a custom bins range so that it displays best the frequency of each move value in 10,000 experiments. hint usings range with floating numbers In [17]: #Write your code here Probability Exercise 1) A sample of four electronic components is taken from the output of a production line. The probabilities of the various outcomes are calculated to be: Pr [0 defectives] = 0.6561, Pr [1 defective] = 0.2916, Pr [2 defectives] = 0.0486, Pr [3 defectives] = 0.0036, Pr [4 defectives] = 0.0001. What is the probability of at least one defective? In [18]: #Method 1 In [19]: #Method 2 2) An oil company is bidding for the rights to drill a well in field A and a well in field B. The probability it will drill a well in field A is 40%. If it does, the probability the well will be successful is 45%. The probability it will drill a well in field B is 30%. If it does, the probability the well will be successful is 55%. Calculate each of the following probabilities: a) What is the probability of a successful well in field A? In [20]: #write your code here b) What is the probability of a successful well in field B? In [21]: #Write your code here c) What is the probability of both a successful well in field A and a successful well in field B? In [22]: #write your code here d) What is the probability of no successful well in field A? In [23]: #write your code here e) What is the probability of no successful well in field B? In [24]: #Write your code here f) What is the probability of no successful well in the two fields together? In [25]: #write your code here g) What is the probability of at least one successful well in the two fields together? In [26] : #Write your code here h) What is the probability of exactly one successful well in the two fields together? In [27]: #write your code here