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Foundations of Probability in Python

中級スキルレベル

更新日 2024/08

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

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PythonProbability & Statistics

5時間

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コース説明

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!

前提条件

Introduction to Statistics in Python

1

Let's start flipping coins

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.

Let’s flip a coin in Python

Flipping coins

Using binom to flip even more coins

Probability mass and distribution functions

Predicting the probability of defects

Predicting employment status

Predicting burglary conviction rate

Expected value, mean, and variance

Calculating the expected value and variance

Calculating the sample mean

Checking the result

Calculating the mean and variance of a sample

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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.

Calculating probabilities of two events

Any overlap?

Measuring a sample

Joint probabilities

Deck of cards

Conditional probabilities

Delayed flights

Contingency table

Total probability law

Formula 1 engines

Bayes' rule

Conditioning

Factories and parts

Swine flu blood test

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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.

Normal distributions

Range of values

Plotting normal distributions

Within three standard deviations

Normal probabilities

Restaurant spending example

Smartphone battery example

Adults' heights example

Poisson distributions

ATM example

Highway accidents example

Generating and plotting Poisson distributions

Geometric distributions

Catching salmon example

Free throws example

Generating and plotting geometric distributions

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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.

From sample mean to population mean

Generating a sample

Calculating the sample mean

Plotting the sample mean

Adding random variables

Sample means

Sample means follow a normal distribution

Adding dice rolls

Linear regression

Fitting a model

Predicting test scores

Studying residuals

Logistic regression

Fitting a logistic model

Predicting if students will pass

Passing two tests

Wrapping up

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Foundations of Probability in Python

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