Probability

Core concepts in probability and statistics with applications to Machine Learning and data analysis.

Topics

Core concepts in probability and statistics with applications to Machine Learning and data analysis.

Notes

Introduction to Probability

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Probability is a measure of how likely an event is to occur. If you throw a fair coin, the probability that it lands on heads is 50 percent (or ). If…

Jun 19, 2026
 

Conditional Probability

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Conditional probability is about calculating the probability of an event happening given that another event has already happened. The key idea is that…

Jun 19, 2026

Bayes Theorem

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Imagine the following scenario. There is a rare disease going around and you want to get tested for it. You go to the doctor and the doctor says: “I…

Jun 20, 2026

Random Variables

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You have seen variables before. In algebra, you may have learned that the variable . It always has the same value. Random variables are different. They…

Jun 21, 2026

Probability Distributions (Discrete)

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In the previous pages, you learned how to calculate individual probabilities and how to do math with them (complements, sums, conditional probability)….

Jun 21, 2026

Probability Distributions (Continuous)

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Now that you know about discrete distributions, let us talk about continuous ones. The key difference:

Jun 22, 2026

Uniform Distribution

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The uniform distribution is the simplest continuous distribution. Imagine a bus that passes every 10 minutes, but you do not know the schedule. You…

Jun 22, 2026

Normal Distribution

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The normal distribution (also called the Gaussian distribution, after Carl Friedrich Gauss) is one of the most important distributions in all of…

Jun 22, 2026

Chi-Squared Distribution

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Imagine you are transmitting bits between two antennas. You send the message 10010. The message travels through the air, which in this case is the…

Jun 22, 2026

Lab: Intro to Pandas

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Welcome to the Pandas tutorial lab. This is the first notebook of the exploratory data analysis (EDA) series, where you will get hands-on practice…

Jun 23, 2026

Lab: Rideshare Exploratory Data Analysis 1

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In this lab you will apply probability, conditional probability, and distributions to a real-world dataset: rideshare trips in Chicago during 2022. You…

Jun 23, 2026

Expected Value, Median, and Mode

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So far you have learned about probability distributions. Now you will learn ways to describe those distributions with single numbers. The most…

Jun 23, 2026

Variance

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The expected value tells you where a distribution is centered, but it does not tell the whole story. Two distributions can have the same mean but look…

Jun 24, 2026

Skewness and Kurtosis

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The expected value and the variance (or standard deviation) paint a good picture of a distribution. However, there are subtleties that they do not…

Jun 24, 2026

Quantiles and Box Plots

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You have learned several ways to describe data numerically: expected value, variance, skewness, and kurtosis. But for a data scientist, it is equally…

Jun 24, 2026

Joint Distributions

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Previously you learned about probability distributions for a single variable (for example, the height of a population). But what if you want to look at…

Jun 25, 2026

Marginal and Conditional Distributions

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Now that you know joint distributions, there are two important operations you can perform on them: finding the marginal distribution and the…

Jun 25, 2026

Covariance and Correlation

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Each distribution has its own expected value and its own variance. But when you have two variables, there is something these measures do not capture:…

Jun 25, 2026

Lab: Rideshare Exploratory Data Analysis 2

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lab

This lab is a continuation of the Week 1 rideshare notebook. In Week 1 you loaded the raw rideshare dataset, performed basic data cleaning, created…

Jun 26, 2026
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