Queen and spade

In this example, you'll use the generalized probability formula \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\) to calculate the probability of two events. Consider a deck of cards (13 cards x 4 suites = 52 cards in total). One card is drawn at random. What is the probability of getting a queen or a spade? Here event A is the card being a queen and event B is the card being a spade. Think carefully about whether the two events have anything in common.

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Statistical Simulation in Python

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Statistical Simulation in Python

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This chapter gives you the tools required to run a simulation. We'll start with a review of random variables and probability distributions. We will then learn how to run a simulation by first looking at a simulation workflow and then recreating it in the context of a game of dice. Finally, we will learn how to use simulations for making decisions.

Exercise 1: Introduction to random variables Exercise 2: np.random.choice()Exercise 3: Poisson random variable Exercise 4: Shuffling a deck of cards Exercise 5: Simulation basics Exercise 6: Throwing a fair die Exercise 7: Throwing two fair dice Exercise 8: Simulating the dice game Exercise 9: Using simulation for decision-making Exercise 10: Simulating one lottery drawing Exercise 11: Should we buy?Exercise 12: Calculating a break-even lottery price

This chapter provides a basic introduction to probability concepts and a hands-on understanding of the data generating process. We'll look at a number of examples of modeling the data generating process and will conclude with modeling an eCommerce advertising simulation.

Exercise 1: Probability basics Exercise 2: Queen and spade

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Exercise 3: Two of a kind Exercise 4: Game of thirteen Exercise 5: More probability concepts Exercise 6: The conditional urn Exercise 7: Birthday problem Exercise 8: Full house Exercise 9: Data generating process Exercise 10: Driving test Exercise 11: National elections Exercise 12: Fitness goals Exercise 13: eCommerce Ad Simulation Exercise 14: Sign up Flow Exercise 15: Purchase Flow Exercise 16: Probability of losing money

In this chapter, we will get a brief introduction to resampling methods and their applications. We will get a taste of bootstrap resampling, jackknife resampling, and permutation testing. After completing this chapter, students will be able to start applying simple resampling methods for data analysis.

Exercise 1: Introduction to resampling methods Exercise 2: Sampling with replacement Exercise 3: Probability example Exercise 4: Bootstrapping Exercise 5: Running a simple bootstrap Exercise 6: Non-standard estimators Exercise 7: Bootstrapping regression Exercise 8: Jackknife resampling Exercise 9: Basic jackknife estimation - mean Exercise 10: Jackknife confidence interval for the median Exercise 11: Permutation testing Exercise 12: Generating a single permutation Exercise 13: Hypothesis testing - Difference of means Exercise 14: Hypothesis testing - Non-standard statistics

In this chapter, students will be introduced to some basic and advanced applications of simulation to solve real-world problems. We'll work through a business planning problem, learn about Monte Carlo Integration, Power Analysis with simulation and conclude with a financial portfolio simulation. After completing this chapter, students will be ready to apply simulation to solve everyday problems.

Exercise 1: Simulation for Business Planning Exercise 2: Modeling Corn Production Exercise 3: Modeling Profits Exercise 4: Optimizing Costs Exercise 5: Monte Carlo Integration Exercise 6: Integrating a Simple Function Exercise 7: Calculating the value of pi Exercise 8: Simulation for Power Analysis Exercise 9: Factors influencing Statistical Power Exercise 10: Power Analysis - Part I Exercise 11: Power Analysis - Part II Exercise 12: Applications in Finance Exercise 13: Portfolio Simulation - Part I Exercise 14: Portfolio Simulation - Part II Exercise 15: Portfolio Simulation - Part III Exercise 16: Wrap Up