CIS192 Python Programming
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1 CIS192 Python Programming Probability, Simulations & Course Wrap-Up Raymond Yin University of Pennsylvania December 8, 2016 Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
2 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
3 The Two Child Problem Suppose I have two children. I announce that I have a son. What is the probability that both children are boys? Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
4 Considering the Possibilities Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
5 Tuesday s Child I announce that I have a son who was born on a Tuesday. Now what is the probability that both children are boys? Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
6 A Handy Visualization Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
7 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
8 Random Variables Definition: A Random Variable is a function from a set of possible outcomes to numeric values. For a coin toss we ve been mapping [lands heads] to 1 and [lands tails] to 0. The values associated with a die roll are the numbers 1 through 6. We will model random variables with "random" Python functions. Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
9 Probability Each random variable has an associated Probability Distribution that maps its values to probabilities. Every probability must be in the interval [0, 1]. The sum of the probabilities must equal 1. We say Pr(X = x) =p to denote the probability of an event. For example, if D represents the outcome of a fair die, Pr(D = 3) = 1 6 Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
10 Expectation E(X) = P x x Pr(x) Where C represents a coin toss as above, E(C) = = 0.5 For a die D, E(D) = = 3.5 Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
11 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
12 The Law of Large Numbers The Weak Law of Large Numbers states that as the number of trials approaches infinity, the frequency of a given outcome approaches its true probability. i.e. If we toss a lot of coins, we will get heads close to half the time. Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
13 Simulations Simulating a situation s possibilities is easy in Python! Use the random library random() returns a float between 0 and 1 uniformly at random randint(a,b) returns a random integer between a and b inclusive choice(li) samples a random element from li sample(li) returns a randomly selected subset of li shuffle(li) randomly permutes the list li uniform(a, b) returns a float uniformly distributed between a and b Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
14 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
15 The Monty Hall Problem You re on a gameshow with Monty Hall! There are three doors in front of you, two have goats behind them and one has a car. After you pick a door, Monty opens another door, revealing a goat. He then gives you the option of switching. Should you switch? Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
16 Monty Hall in Python def monty(switch = False): car = randint(1,3) pick = randint(1,3) opened = choice(list({1, 2, 3} - {car, pick})) if switch: pick = choice(list({1, 2, 3} - {pick, opened}) ) if pick == car: return "Car" else: return "Goat" Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
17 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
18 Topics We ve Covered Python Basics & Fundamentals Functional Programming Object-Oriented Programming Iterators, Generators, Exceptions & IO Regular Expressions & Other Modules HTTP Requests / HTML Parsing Data Analysis Machine Learning Natural Language Processing Web Apps Artificial Intelligence Probability & Simulations Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
19 Outline 1 Probability and Simulations The Two Child Problem Basic Definitions The Law of Large Numbers Monty Hall in Python 2 Looking Forward CIS 192 in Review Next Steps Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
20 Scratching the Surface Each special topic has MUCH more depth than what we ve covered this semester. Many topics we haven t mentioned Parallel & Distributed Computing Concurrency Graphical User Interfaces Testing Frameworks etc. Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
21 What s Next? I hope you find the skills you ve acquired from CIS 192 useful! Build your own side-projects, big or small! Learn more about Python! PyCon conference recordings Obey the Testing Goat (TDD in Python + Web Dev) New Coder: practical tutorials in Python Join the Python community! /r/python subreddit Trending GitHub Python repositories StackOverflow Python questions Raymond Yin (University of Pennsylvania) CIS 192 December 8, / 21
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