Python Tutorial: Statistical Simulation in Python

hi I'm Tushar Shankar your instructor for this course I'm a data scientist and have worked at companies like uber Airbnb and LinkedIn in this course we'll learn about statistical simulation using Python simulations are a powerful and practical tool for solving a wide variety of data science problems I have personally utilized simulations for addressing many complex challenges and would highly recommend adding it to your arsenal of statistical methods in this course we'll start with the basics of random variables and run our first simulation will then learn to use simulations for estimating probability following that we'll familiarize ourselves with extremely useful bootstrapping and resampling methods for data analysis finally we'll dive deeper into more advanced applications let's start with some basics a random variable is a quantity that can take on multiple values based on random chance when the variable can take on infinitely many values it's called a continuous random variable think about the height of a person although the height lies within some reasonable limits on average the actual value could have infinite possibilities in that interval that is why we term it as a continuous random variable similarly if the variable can only take a finite set of values it is called a discrete random variable the rule of a six-sided die can have only one of six possible outcomes and as was considered a discrete random variable next let's look at probability distributions a probability distribution is a mapping from the set of possible outcomes of a random variable to the probability of observing that outcome it tells you how likely you are to observe a given outcome or a set of outcomes just like random variables probability distributions are either discrete or continuous depending on the type of random variable they represent for continuous random variables the distribution is represented by a probability density function and probability is typically defined over an interval the normal distribution is an example of a continuous distribution for discrete random variables the distribution is represented by a probability mass function and probability can be defined at a single point or over an interval among discrete distributions binomial and Poisson distributions are widely used Pythons numpy random module is a robust and flexible tool that lets us work with random variables by now you should have a good understanding of random variables and their relation to probability distributions let's put these concepts to practice and work through some exercises