7 Probability Distributions

Probability not only helps us understand how likely an event is to occur, but also forms the foundation of many statistical methods used for decision-making. When a process or experiment produces varying outcomes, we use a random variable to represent those outcomes and a probability distribution to describe how the probabilities are assigned to each possible value. Understanding the shape and properties of a distribution is essential because it determines how data behave, how we calculate probabilities, and how we make predictions. From distributions for continuous variables to the behavior of statistics such as sample means, probability distributions serve as the core of inferential statistics.

This material will guide you through several key concepts:

Probability distributions for continuous variables, which describe the likelihood of values over a continuous range.
Sampling distributions, which represent the distribution of sample statistics such as the sample mean or sample proportion.
The Central Limit Theorem (CLT), one of the most important results in statistics, explaining why the distribution of sample means tends to be normal regardless of the population’s underlying shape.
Sample proportion distributions, widely used in survey analysis and quantitative research.

Each section is supported with video explanations to enhance conceptual understanding. By mastering these topics, you will be better equipped to analyze data, build statistical models, and draw conclusions based on solid probabilistic principles.