1. Probability Models and Axioms
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it as part of Tsitsiklis's free MIT probability lectures, recommended alongside the Bertsekas and Tsitsiklis textbook.
Recommended by 3 people across 3 different months, 2014 to 2021.
What it is
The first lecture of MIT 6.041 Probabilistic Systems Analysis and Applied Probability (Fall 2010), taught by John Tsitsiklis. It introduces probability models, sample spaces and the basic axioms of probability.
What people said
Recommends Cookie · 2015-02 · Mathematics Stack Exchange · on “What is the Spivak of Probability?”
Introduction to Probability [LINK] by Dimitri P. Bertsekas and John N. Tsitsiklis The authors are MIT professors. Here are probability lecture notes [LINK] written by the authors themselves. Here are also video lectures on Youtube [this video] by Tsitsiklis. (Thanks @dietervdf for pointing that out.)
Recommends hanugm · 2017-10 · Mathematics Stack Exchange · on “Different types of sample spaces in probability”
In probability, sample space is a set of all possible outcomes of an experiment. A sample space can be finite or infinite. A sample space can be discrete or continuous. A sample space can be countable or uncountable. From some texts I got that finite sample space is same as discrete sample space and infinite sample space is continuous sample space . But some texts are saying that countable sample space is discrete sample space and uncountable sample space is continuous sample space . Which one of the following above is correct? I got confuse because of the following two statements in this text book [LINK] Discrete Probability Law : If the sample space consists of a finite number of possible
Recommends iamsad · 2021-10 · Mathematics Stack Exchange · on “Doubt in an approach to solve a probability question”
If you multiply by 3! you are over-counting. You're basically counting frontseat, frontseat, backseat as different from frontseat, frontseat, backseat (you are permuting the two frontseat picks and counting them as different even though you shouldn't be). The reason is that when you assign a 4/6 probability to picking a frontseat on your first pick, you are taking care of all ordered ticket outcomes for which the first seat you picked was a frontseat. What you should really do is calculate the probability that you obtain frontseat, frontseat, backseat + frontseat, backseat, frontseat + backseat, frontseat, frontseat. This is because there are 3 different ways that you could have chosen the t
Cites Kartik · 2014-07 · Mathematics Stack Exchange · on “Examples of figures whose area depend on axiom of choice”
Many times I have heard that there are some 'figures' whose area is not fixed and they depend on axiom of choice. For example, In this answer [LINK] . In this lecture about probabilty [this video] . I did not know what is axiom of choice, but after reading the wikipedia article and this question: Axiom of Choice Examples [LINK] , I have understood a little bit about it but still I don't understand it completely. Can anyone please provide some simple examples of these figures and why Axiom of choice is needed for them?