# Statistical Simulation in Python

Learn to solve increasingly complex problems using simulations to generate and analyze data.

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## Course Description

## Get to Grips with Random Variables

Simulations are a class of computational algorithms that use random sampling to solve increasingly complex problems. Although simulations have been around for a long time, interest in this area has recently grown due to the rise in computational power and the applications across Artificial Intelligence, Physics, Computational Biology and Finance just to name a few.This course provides hands-on experience with simulations using real-world applications, starting with an introduction to random variables and the tools you need to run a simulation.

## Gain an Introduction to Probability Concepts

The second chapter in this course provides an overview of probability concepts, using practice exercises based on card games and well-known probability puzzles to provide a framework for your new knowledge. You’ll finish this chapter by modeling an eCommerce advertising simulation.## Discover Resampling Methods and Applications

The third chapter looks at different resampling methods, including bootstrap resampling, jackknife resampling, and permutation testing. Once you’ve completed this course, you’ll be able to add these methods to your data analysis process.## Learn to Use Simulation for Business and Build Your Portfolio

Simulation has many real-world applications, especially in the world of business. The final chapter in this course looks at these, and takes you through a business planning problem to get you used to using your new skills in a business setting. You’ll look at modeling profits, optimizing costs, and getting started with power analysis.For Business

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### Basics of Randomness & Simulation

**Free**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.

Introduction to random variables50 xpnp.random.choice()50 xpPoisson random variable100 xpShuffling a deck of cards100 xpSimulation basics50 xpThrowing a fair die100 xpThrowing two fair dice100 xpSimulating the dice game100 xpUsing simulation for decision-making50 xpSimulating one lottery drawing100 xpShould we buy?100 xpCalculating a break-even lottery price100 xp - 2
### Probability & Data Generation Process

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.

Probability basics50 xpQueen and spade50 xpTwo of a kind100 xpGame of thirteen100 xpMore probability concepts50 xpThe conditional urn100 xpBirthday problem100 xpFull house100 xpData generating process50 xpDriving test100 xpNational elections100 xpFitness goals100 xpeCommerce Ad Simulation50 xpSign up Flow100 xpPurchase Flow100 xpProbability of losing money100 xp - 3
### Resampling Methods

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.

Introduction to resampling methods50 xpSampling with replacement50 xpProbability example100 xpBootstrapping50 xpRunning a simple bootstrap100 xpNon-standard estimators100 xpBootstrapping regression100 xpJackknife resampling50 xpBasic jackknife estimation - mean100 xpJackknife confidence interval for the median100 xpPermutation testing50 xpGenerating a single permutation100 xpHypothesis testing - Difference of means100 xpHypothesis testing - Non-standard statistics100 xp - 4
### Advanced Applications of Simulation

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.

Simulation for Business Planning50 xpModeling Corn Production100 xpModeling Profits100 xpOptimizing Costs100 xpMonte Carlo Integration50 xpIntegrating a Simple Function100 xpCalculating the value of pi100 xpSimulation for Power Analysis50 xpFactors influencing Statistical Power50 xpPower Analysis - Part I100 xpPower Analysis - Part II100 xpApplications in Finance50 xpPortfolio Simulation - Part I100 xpPortfolio Simulation - Part II100 xpPortfolio Simulation - Part III100 xpWrap Up50 xp

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Prerequisites

Sampling in PythonTushar Shanker

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