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15 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I think you should (and likely will have to) use the assigned text and approach. It's incredibly unlikely you will just derive some new approach. That's not how high school teaching works. And on ...
Pro-pedagogy guest troll's user avatar
10 votes
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Special topics for introductory probability

A classic application of Bayes' Theorem is in medical testing, and the difference/conversion between "what is the probability I test positive, given I have the condition" vs. "what is ...
Kevin P. Costello's user avatar
9 votes
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Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I would recommend avoiding foundational issues when teaching probability at a low level. At the high school level one mostly deals with finite probability spaces and the normal distribution. The ...
Dan Fox's user avatar
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9 votes
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How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

I think you will want to start by convincing the audience that $p(aX+b = ax_i + b)$ is equal to $p(X=x_i)$, probably with examples. I am not an expert statistician so please let me know politely if I ...
Chris Cunningham's user avatar
9 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I'm not familiar with Cox approach at all, so I cannot provide a qualified comparison, but I find the Kolmogorov's axioms pretty easy to comprehend and use and I'll try to explain why. No matter what ...
fedja's user avatar
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8 votes

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

This is a consequence of the definition of the variance (1) the linearity of expectation (2) and an algebraic manipulation (3): $$V(aX+b)\stackrel{(1)}{=}\mathbb{E}(aX+b-\mathbb{E}(aX+b))^2\stackrel{(...
Kostya_I's user avatar
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6 votes
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Correct notation of a Sample space

It's true that you typically refer to a random variable by a capital letter (e.g., $X$) and a particular value by a lowercase letter (e.g., $x$). So, $P(X = x)$ would represent the probability that ...
Justin Skycak's user avatar
6 votes

Special topics for introductory probability

One example of elementary probability is the so-called Birthday problem which asks for the probability that in a room of $n$ people two will share the same birthday. Sometimes formulated as a paradox ...
mdewey's user avatar
  • 311
6 votes

Special topics for introductory probability

You might already be aware of this one, given how famous it is, but the first thing that comes to my mind is the Monty Hall Problem. It doesn't require any fancy mathematical machinery, just a basic ...
Justin Skycak's user avatar
6 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students? My answer is: No, you should not do that. These theoretical ...
Daniel R. Collins's user avatar
5 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

"I am planning to become a math high-school teacher" So it seems to me that you expect too much from high school students. I made the same mistake, the true is the vast majority of them will ...
Marcel Espinosa's user avatar
5 votes

Special topics for introductory probability

Bertrand's Paradox is an old saw. The point is that trying to randomize an experiment is tricky since there can be different points of view.
MaxW's user avatar
  • 151
5 votes
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Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

I'd say (time permitting) put it to a practical test. Take a standard 6-sided die, say you're going to roll it 100 times. You (the instructor) guess "1" every time, while the student can ...
Daniel R. Collins's user avatar
3 votes

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

Do it in two easy steps: Prove that $V[X+b]=V[X]$. This one is easy to prove since variance is a measure of deviation from the mean, hence change of origin will not affect it. Mathematically, $ E({X+...
whoisit's user avatar
  • 131
3 votes

The easy and the hard problems involving independent events

I always figured the point of these exercises is to show that even if two events turn out to be independent, it doesn't mean that the underlying random variables are uncorrelated / independent. Kind ...
Justin Skycak's user avatar
3 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

How probable is it that a $1$ will appear when you throw a die? How probable is it that there was life on Mars a billion years ago? For the first question, one can say $1/6$ because it happens one-...
Michael Hardy's user avatar
3 votes

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

In Economics of past decades, an analogous issue arose as regards teaching "the neoclassical paradigm" versus teaching the "Keynsian paradigm". In a pretty realistic approach ...
Alecos Papadopoulos's user avatar
2 votes

Special topics for introductory probability

I would look ar some of the basic six sigma literature and at doe. It is connected to all kinds of factory snd other process improvement. Very clear business connection. I would eschew the Bayesian ...
Guest poster's user avatar
2 votes
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PROBABILITY QUESTION

This sounds like a homework question, but it seems you're a professor with publications and years of history on the site, so I'll give you the benefit of the doubt and assume you're asking for a good ...
Justin Skycak's user avatar
2 votes

Correct notation of a Sample space

There is no correct here. While it is common to use capital letters for random variables and the corresponding lowercase letters for the values they assume, this convention is not a strong one and ...
Dan Fox's user avatar
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2 votes

The easy and the hard problems involving independent events

Suppose $X_1,\ldots,X_n$ are independent normally distributed random variables with expected value $\mu$ and variance $\sigma^2.$ Let $\overline X = \text{the sample mean} = (X_1+\cdots+X_n)/n$ and $S^...
Michael Hardy's user avatar
1 vote

Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

Did you consider the fact that your students have a point? When playing the lottery, let's say that the numbers $1$, $2$ and $3$ are popular, while $4$ is not. Being a popular number means that ...
Dominique's user avatar
  • 2,165
1 vote

Special topics for introductory probability

[Additional to previous answer--can't edit, sorry.] dt688: I would be very wary about being too difficult or particular, when teaching in a corporate environment. I.e. if GMers are your target ...
Guest poster on another device's user avatar
1 vote

Online Probability Simulation for Compound Events

It's really easy to write a script to do this, so I wrote one for you that runs entirely in the browser and allows you to edit the sample space elements: https://www.pythonmorsels.com/p/24dps/ Just go ...
Justin Skycak's user avatar
1 vote

Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students

There was a question "is throwing dice a deterministic or stochastic process" on Physics.SE a while back, and I think this answer is insightful and accessible enough to spur a good ...
Justin Skycak's user avatar
1 vote

How to explain that winning the lottery is not a 50/50 distribution?

Roll a die. Say, it will either roll a "1" or not, right? So the probability of rolling a "1" is 50%, yes? Say, it will either roll a "2" or not, right? So the ...
Torsten Schoeneberg's user avatar

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