# Foundations of Probability in Python

Learn fundamental probability concepts like random variables, mean and variance, probability distributions, and conditional probabilities.

5 Hours16 Videos61 Exercises
10,100 Learners

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## Course Description

Probability is the study of regularities that emerge in the outcomes of random experiments. In this course, you'll learn about fundamental probability concepts like random variables (starting with the classic coin flip example) and how to calculate mean and variance, probability distributions, and conditional probability. We'll also explore two very important results in probability: the law of large numbers and the central limit theorem. Since probability is at the core of data science and machine learning, these concepts will help you understand and apply models more robustly. Chances are everywhere, and the study of probability will change the way you see the world. Let’s get random!
1. 1

### Let's start flipping coins

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A coin flip is the classic example of a random experiment. The possible outcomes are heads or tails. This type of experiment, known as a Bernoulli or binomial trial, allows us to study problems with two possible outcomes, like “yes” or “no” and “vote” or “no vote.” This chapter introduces Bernoulli experiments, binomial distributions to model multiple Bernoulli trials, and probability simulations with the scipy library.

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Let’s flip a coin in Python
50 xp
Flipping coins
100 xp
Using binom to flip even more coins
100 xp
Probability mass and distribution functions
50 xp
Predicting the probability of defects
100 xp
Predicting employment status
100 xp
Predicting burglary conviction rate
100 xp
Expected value, mean, and variance
50 xp
Calculating the expected value and variance
50 xp
Calculating the sample mean
100 xp
Checking the result
100 xp
Calculating the mean and variance of a sample
100 xp
2. 2

### Calculate some probabilities

In this chapter you'll learn to calculate various kinds of probabilities, such as the probability of the intersection of two events and the sum of probabilities of two events, and to simulate those situations. You'll also learn about conditional probability and how to apply Bayes' rule.

3. 3

### Important probability distributions

Until now we've been working with binomial distributions, but there are many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial distribution: the normal, Poisson, and geometric distributions.

4. 4

### Probability meets statistics

No that you know how to calculate probabilities and important properties of probability distributions, we'll introduce two important results: the law of large numbers and the central limit theorem. This will expand your understanding on how the sample mean converges to the population mean as more data is available and how the sum of random variables behaves under certain conditions. We will also explore connections between linear and logistic regressions as applications of probability and statistics in data science.

Collaborators

Prerequisites

Introduction to Statistics in Python  Alexander A. Ramírez M.

CEO at Synergy Vision

Alexander is the CEO @ Synergy Vision which focuses on financial data science providing services to Banks, Insurance companies and Brokerages. He is a Computer Engineer from Universidad Simón Bolivar (USB) with 22 years of experience with a master degree in Random Models and he is working in a Doctorate in Mathematics at Universidad Central de Venezuela (UCV).
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