The Central Limit Theorem and Inverse Transform Sampling
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Random Variables and Probability Distributions
A random variable represents the result of some random process, like flipping a coin, rolling dice, or spinning a bottle. They can be discrete and take on only certain values (like heads or tails, or 1, 2, 3, 4, 5 or 6 on a die) or continuous and take on any real value (like the […]
The Central Limit Theorem
The Central Limit Theorem is a pretty important concept in statistics. It states that, even if the original probability distribution isn’t normal, the mean of the samples taken from this distribution is distributed normally as the number of samples increases. What does this mean? Let’s try an experiment. You’re going to need python (I’m using […]
Experiments, Hypothesis Testing, and Power
Hypothesis tests are a test you do when you wanna find out about something in the world. You make a hypothesis, then you test it against another hypothesis, and see which one is less wrong. Sometimes they’re called A/B tests (usually in business or marketing), but this is the same idea. You have two options, […]
Logarithms
The logarithm is a mathematical function that is related to the power function. The power function takes a number and multiplies it by itself a number of times, like 2 to the 2nd power (22) is 4 or 10 to the 3rd power (103) is 1000. The logarithm is the reverse of that. It’s kind […]
A Primer on Probability
Note This post is a work-in-progress, but I wanted to publish this early so I could link to it in my other posts. The Basics Probability is the likelihood that an event will happen. If I have a fair coin, then there’s a 50/50 chance it will land heads or tails. Each has a 50% […]
(Re)Learning Machine Learning – Logistic Regression
This time we’re going to do logistic regression. Logistic regression uses the same idea as linear regression (see my previous post) to classify input as one of two different classes. Instead of a linear function (one that looks like a straight line) we use a log-based function (making it “logistic”), and even though we’re using […]
(Re)Learning Machine Learning – Linear Regression
I am writing this as I relearn the basics of machine learning to record my thoughts and hopefully help someone (probably me) in the future. I find that I learn best when I implement the algorithms myself, even if I have to make less-efficient versions of built-in functions that many tutorials gloss over. If you’d […]