Probability and Statistics: an introduction by Norman J. Wildberger

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source: njwildberger     2013年9月28日
This is the first lecture of a short course introducing probability and statistics, meant for an advanced first year undergraduate class. The course will be about 8 lectures long, and will go from basic sets, counting, probability and odds, to probability measures, conditional probabilities, Bayes rule, random variables, probability distributions (discrete and continuous), mean, variance, Binomial, Poisson, normal distributions, and perhaps some words in the direction of the Central Limit Theorem. We will not discuss inference in this course, so it is a rather limited, specific introduction to the subject.
In this lecture I review some basic notation and terminology for sets, including operations and rules, the Inclusion/Exclusion principle and partitions; together with some basic facts about functions.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

Probability and Statistics: an introduction
A brief introduction to Probability and Statistics. This short course will be aimed at advanced first year undergraduates, with good algebraic skills and some knowledge of calculus. We will discuss probabilities and odds, random variables, probability distributions (both discrete and continuous), for example the Binomial, Poisson and normal distributions, mean and variance and mention the Central Limit Theorem.

1: Review of sets and functions 51:26
2: Basic Counting and Probability 49:53
3: Probabiilty spaces, events and conditional probabilities 49:22
4: Total probability, Bayes' rule and tree diagrams 52:09
5: Random variables, means, variance and standard deviations 53:09
6: Binomial and geometric distributions 52:22
7: The sign rule and continuous probability distributions 50:15
8: The normal distribution 48:24