The normal distribution | Probability and Statistics | NJ Wildberger

In this final lecture in this short introduction to Probability and Statistics, we introduce perhaps the most important probability distibution: the normal distribution, also known as the `bell-curve'. Its role is clarified by the Central Limit theorem, a key result in Statistics, that states roughly that if you sample an arbitrary probability distribution, discrete or continuous, then the averages of that sample end up resembling more and more a normal distribution as the number of terms in the sample increases. Here we start with the standard normal, which has mean 0 and variance 1. Although we cannot compute probabilities directly with it, in the sense of evaluating integrals precisely, we can do so approximately. The Cumulative distribution function is a useful tool in helping us do this--essentially just the integral of the probability density function. A general normal distribution is related to a standard normal via an affine transformation, and I explain how to go from one to another: the idea being that questions about a general normal distribution are usually converted to standard normal questions, and the answers converted back. Thanks for watching the series! ************** Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon:   / njwildberger   Your support would be much appreciated. Insights into Mathematics YT channel:    / njwildberger   Insights into Mathematics Playlists:    • The Algebra of Boole, Logic and Circuit An...   (31 videos)    • Box Arithmetic: a new framework for Mathem...   (18 videos)    • Hypergroups and Diffusion Symmetry: an int...   (6 videos)    • Rational Trigonometry for maths, physics a...   (4 videos)    • Sociology and Pure Maths   (44 videos)    • Old Babylonian mathematics and Plimpton 322   (8 videos)    • Math Foundations   (226 videos)    • Math Seminars N J Wildberger   (26 videos)    • Math History (ancient to modern)   (45 videos)    • Geometric Linear Algebra   (43 videos)    • Algebraic Topology   (40 videos)    • Universal Hyperbolic Geometry   (55 videos)    • Differential Geometry   (34 videos)    • Elementary Probability and Statistics   (8 videos)    • Math Terminology for Incoming Uni Students   (9 videos)    • Famous Math Problems   ( 46 videos) Wild Egg Maths Playlists:    • Box Arithmetic Book: A finite multiset fou...   (NEW!!)    • Intro to Algebraic Calculus with Box Arith...   (4 videos)    • Classical to Quantum (for Members)   (64 videos)    • Solving Polynomial Equations and the Geode...   (45 videos)    • De Casteljau Bezier curves and associated ...   (20 videos)    • Exploring q-series (for Members)   (8 videos)    • Six: A mathematical exploration   (9 videos)    • Algebraic Calculus One: a new foundation f...   (52 videos)    • Advice to prospective research mathematici...   (9 videos)    • The Hexagrammum Mysticum: a Geometric Gem ...   (14 videos)    • Algebraic Calculus Two   (8 videos)    • Special (Polynomial) Functions and Maxel N...   (25 videos)    • Dynamics on Graphs: The ADE Phenomenon & B...   (30 videos)