edX
edXProbability and Statistics III: A Gentle Introduction to Statistics
194 studentsINTERMEDIATEEnglish
Korshub's take
The Foundation: Distributions and the Central Limit Theorem
Statistics only makes sense once you understand distributions. This course builds your intuition by walking through a library of probability distributions—binomial, Poisson, exponential, normal, and others—showing you where each one naturally arises and why it matters.
The course reserves special emphasis for the Central Limit Theorem, a result so important it deserves the attention. Once you truly grasp it, you'll understand why so much of statistical inference hinges on the normal distribution, and why you can make probability statements about averages and sums even when the underlying data is messier. After distributions, you'll learn estimation methods (how to infer a population parameter from a sample) and meet the t, chi-squared, and F distributions that underpin hypothesis testing. It's a complete tour of the mathematical foundations you'll use in applied statistics.
About this course
This course provides an introduction to basic statistical concepts.
We begin by walking through a library of probability distributions, where we motivate their uses and go over their fundamental properties.
These distributions include such important folks as the Bernoulli, binomial, geometric, Poisson, uniform, exponential, and normal distributions, just to name a few. Particular attention is paid to the normal distribution, because it leads to the Central Limit Theorem (the most-important mathematical result in the universe, actually), which enables us to make probability calculations for arbitrary averages and sums of random variables.
We then discuss elementary descriptive statistics and estimation methods, including unbiased estimation, maximum likelihood estimation, and the method of moments – you gotta love your MoM! Finally, we describe the t, X2, and F sampling distributions, which will prove to be useful in upcoming statistical applications.
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