Sampling Distribution of the Sample Proportion
🎯 The Sampling Distribution of the Sample Proportion In a population, the proportion is the number of successful outcomes over the total number of cases. This proportion is denoted by \( \beta \...
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🧱 What You’ll Learn Here
đź“Š Foundations
Clear explanations of the statistics, linear algebra, and calculus you actually need — no more, no less.
🤖 ML Concepts
Build up from intuitive models to CNNs and neural networks — explained visually and step-by-step.
🧠Problem Solving
Practice with real problems, detailed solutions, and structured problem-solving roadmaps.
Population, Sample, and Sampling Distributions Explained
🎯 Population Distribution The population distribution describes the values of a variable for all members of a population. Mean: \( \mu \) (population mean) Standard deviation: \( \sigma \)...
Understanding the Sampling Distribution of the Sample Mean and the Central Limit Theorem
🎯 Simple Random Samples and Sampling Distribution When working with samples, the Simple Random Sample (SRS) is key — each sample must be a simple random sample. If you take a set of samples, ea...
From Sample to Population: Basics of Sampling in Statistics
🎯 What’s the Difference Between a Population and a Sample? In statistics: The population refers to the entire group we want to study or draw conclusions about. A sample is a subset of that...
Understanding Binomial Distribution
🎯 What is Binomial Distribution? The Binomial Distribution is a discrete probability distribution used to model the number of successes in a fixed number of independent experiments — where each ...
Understanding Z-Distribution and Using the Z-Table
đź“Ś What is Z-Distribution? The Z-distribution (or standard normal distribution) is a special case of the normal distribution with: Mean \( \mu = 0 \) Standard deviation \( \sigma = 1 \) I...
Understanding Normal Distribution
đź“Ś What is Normal Distribution (Gaussian Distribution)? The normal distribution (or Gaussian distribution) is a type of continuous probability distribution for a real-valued random variable. It d...
Mean, Variance, and Standard Deviation of Random Variables
How do we summarize a random variable with a single number? What happens to the mean and variance if we shift or scale the variable? This post explains the mean, variance, and standard deviation fo...
What Are Random Variables and How Do We Visualize Their Distributions?
How can we model the outcome of a random process? What’s the difference between discrete and continuous probability? And how do we visualize all of that? This post answers these questions — with i...
Understanding Independence and Bayes’ Rule
How can we tell if two events are independent? What does it mean to update our beliefs when new data comes in? This post unpacks these ideas — and ends with a walkthrough of Bayes’ Rule. 📚 Th...
Making Sense of Probabilities: Union, Tables, and Conditional Thinking
How can we combine probabilities when events overlap? What do those totals in a table mean? Let’s break it all down — and build toward smarter probability thinking. 📚 This post is part of the...
How Random Is Random? Understanding Probability and Events
Ever flipped a coin and wondered: Shouldn’t it be 50/50? Then why did I get 3 heads in a row? Welcome to the world of randomness — where short-term surprises often give way to long-term predictabi...
Regression: Predicting Relationships Between Variables with the Best Fit Line
In our last post, we explored Pearson’s r, which measures the strength and direction of a linear relationship between two variables. Now, we take the next step: using regression to model and predic...
Pearson’s r: Measuring the Strength and Direction of Linear Relationships
Understanding the relationship between two variables is crucial in data analysis. While scatter plots help us visualize this relationship, they don’t give us an objective measure of strength or dir...
Conditional vs. Marginal Proportions: What’s the Difference?
Have you ever looked at a data table and wondered: ❓ What’s the difference between marginal and conditional proportions? ❓ When do I use each one? You’re not alone! These two terms come up a ...