Questions tagged [paradox]
A paradox is a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
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Doubling your accuracy - extension
Frederick Mosteller's 50 Challenging Problems in Probability has a nice question I have not seen before, and I was wondering whether it could be extended.
49. Doubling your accuracy
An unbiased ...
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Is it possible to define conditional probability to avoid the Kolmogorov Borel paradox?
Kolmogorov defines conditional probability for density distributions in 'foundations of the theory of probability' chapter 5 equation 1.
The conditional probability or density is such a function that ...
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How to make decisions when statistics provide completely different conclusions when viewed from different perspectives?
One can look at a statistic from two different perspectives and come to two completely opposite conclusions.
Consider how Radon gas in homes contributes to lung cancer.
The danger is linearly ...
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Can obesity paradox among subjects with cardiovascular disease be explained by incorrectly controlling for a mediator?
Given the following causal diagram:
Obesity -> Cardiovascular disease -> Mortality
which follows from obesity being a causal factor of cardiovascular disease (CVD), isn't it reasonable to ...
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Applying Bayesian probability to a generalized Monty Hall problem
I posted this question about the Monty Hall problem and Monty's knowledge of the probability distribution several months ago. I got some good answers and this one in particular helped me gain some ...
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A seeming paradox regarding estimation of the number of buttons
There is a computer with $N$ buttons in a secret room. We do not have access to the computer and we do not know $N$. But we know that $N\leq 100$ and we have a ever so slightly larger prior for ...
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In the Monty Hall problem, does it matter that the host knows which door the car is behind? If so, why?
If I'm thinking about this correctly, regardless of how the host chooses which door to open, there's a 1/3 chance the player initially picks the door with the car behind it, in which case they shouldn'...
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How to resolve the ambiguity in the Boy or Girl paradox?
Specifically, I was reading this article, which discusses this wording of the question:
Consider a family with two children. Given that one of the children is a boy, what is the probability that both ...
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Is the sleeping beauty paradox really one? [duplicate]
See en.wikipedia.org/wiki/Sleeping_Beauty_problem for the statement of this problem.
This seems to me to be a simple weighted average problem. Because the total number of days awake varies between 1 (...
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Causal Inference - when Conditioning on a Collider is correct
I have been reading Judea Pearl's Book of Why and in it, he tackles the famous Monty Hall problem through a causal lens. Although it may still grind away at our initial instincts, hopefully nobody ...
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simulating the St. Petersburg Paradox [duplicate]
from the following simulation it seems the fee I am willing to pay should be smaller than 10, instead of $\infty$, differs from the paradox, what is happening here?
Edit:
For those that aren't ...
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What is actually Galton's paradox?
From One Thousand Exercises in Probability I found the exercise:
Galton's paradox. You flip three fair coins. At least two are alike, and it is an even chance that the third is a head or a tail. ...
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St. Peterbourg paradox - expected value of both players
Im reading a paper by Karl Menger about the St. Peterbourg paradox (see below): his point is that the paradox does not rely on a mathematical expectation of infinite value, but on the discrepancy ...
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Conflict between significance and importance. A paradox
When examining a set of proteins of healthy controls and patients I found significant differences using the Mann-Whitney test. However, when I used Random Forest, the most 'important' proteins for ...
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Can Lord's paradox be caused by regression to the mean?
I am trying to understand Lord's paradox, where controlling for baseline status can affect inference. I tried to set up some data following the quotation in Wikipedia
“A large university is ...
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Sum of individual parts not adding up to the whole
I am analyzing the WoW change in conversion rate (visitors who booked / visitors).
Let's say the WoW change from week 1 to week 2 was -10% (dropped 10%). Now, I want to know what/where this drop in ...
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Borel Cantelli conceptual problem
I recently learned about the Borel-Cantelli lemmas and although I could follow the derivation and it seems watertight, I have a problem wrapping my head around its implication. I hope you can tell me ...
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Extremely Long Runs in Bernoulli Process
I caught my son counting his ribs during a biology exam. As punishment for this act of cheating, I set him in the corner with a fair coin and told him he must stay in the corner, flipping the coin, ...
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How can the nicest men in the conditioned subset be as nice as the average person in the whole population?
I don't grasp the bolded sentence beneath from Jordan Ellenberg's article. His diagram no longer renders, so I use these.
How can the nicest men in the green triangle be as nice as the whole ...
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Bayesian comparison of differing model size
This issue is related to a real problem, but I've boiled down to a minimal example.
Simplest version
Suppose I get to observe two variables, $X_1$ and $X_2$. We can think of these data being ...
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Paradox game for life and death
This is probably not new to any student of statistics - yet I can't find the name of that "paradox" to search for.
Imagine the richest person on earth holds a game:
A participant is invited to roll ...
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Famous easy to understand examples of a confounding variable invalidating a study
Are there any well-known statistical studies that were originally published and thought to be valid, but later had to be thrown out due to a confounding variable that wasn't taken into account? I'm ...
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Did Jaynes ever comment on Lindley’s paradox?
I wondered whether ET Jaynes ever wrote or expressed an opinion about Lindley’s famous statistical paradox? I would be curious about his take on it, and imagine he must have done since he wrote ...
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How to program a Monte Carlo simulation of Bertrand's box paradox?
The following problem has been posted on Mensa International Facebook Page:
$\quad\quad\quad\quad\quad\quad\quad\quad$
The post itself received 1000+ comments but I won't go into details about the ...
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At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
The question (slightly modified) goes as follows and if you have never encountered it before you can check it in example 6a, chapter 2, of Sheldon Ross' A First Course in Probability:
Suppose that ...
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