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2 votes
1 answer
621 views

Does some published texbook take a particular approach (described here) to the transition from discrete to continuous probability distributions?

(I posted this question at matheducators.stackexchange.com and it seems to be considered an inappropriate question for that site. I don't understand why.) Imagine an introductory probability course ...
Michael Hardy's user avatar
55 votes
16 answers
15k views

Why do we need random variables?

In this MathStackExchange post the question in the title was asked without much outcome, I feel. Edit: As Douglas Zare kindly observes, there is one more answer in MathStackExchange now. I am not ...
Filippo Alberto Edoardo's user avatar
12 votes
12 answers
2k views

What are fun elementary subjects in probability?

I have to read several lectures on probability or applications of probability for high school students (of high level). There is no necessary part I must lecture, that is, my aim is just advertisement....
20 votes
2 answers
4k views

Teaching stochastic calculus to students who know no measure theory (or PDE, or...)

I've got quite a challenge as my teaching assignment for the next Fall (not that I want to get rid of it, quite the contrary, but I still feel like asking for advice won't hurt :-)). I'm to teach the ...
fedja's user avatar
  • 60.9k
3 votes
2 answers
646 views

Can this informal argument (for the fact that almost all reals in the unit interval are irrational) be saved?

In the textbook from which I am teaching a Discrete Math course, the authors propose randomly generating an infinite sequence of decimal digits $d_1, d_2, \dots$. We are to think of this as the ...
Hugh Thomas's user avatar
  • 6,210
11 votes
2 answers
3k views

Good examples of random variables whose image is not a measurable set?

Are their simple/natural examples of real-valued Borel-measurable random variables whose image is not a Borel set? Something that occurs "naturally"? I am teaching Doob's lemma (for two real-valued ...
Uwe Franz's user avatar
  • 2,191
9 votes
4 answers
1k views

Characterization of the Poisson law

This semester, I teach an introduction to probability course tailored for students with no science background and so with very very little prerequisites. We started with the basics of analytic ...
Olivier's user avatar
  • 10.6k
2 votes
2 answers
6k views

Examples of random variables

I'm looking for a list of examples of random variables to use in teaching a measure-theoretic probability course. For example, the Rademacher functions are an explicit construction of independent ...
John D. Cook's user avatar
  • 5,177