All Questions
Tagged with paradoxes probability-theory
23
questions
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69
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Lack of strong law for the Saint Petersburg paradox
The Saint Petersburg paradox can be formulated as follows: Suppose we have a lottery whose payout ${X}$ takes taking values in the powers of two ${2,2^2,2^3,\dots}$ with
$\displaystyle {\bf P}( X = 2^...
- 1,011
10
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1
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975
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How to show that the event that a prisoner does not go free is not measurable
I was reading this webpage a few months ago about the following problem-
A countable infinite number of prisoners are placed on the natural numbers, facing in the positive direction (ie, everyone can ...
- 25.7k
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64
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Variation of St. Petersburg Paradox
I was discussing the the St. Petersburg paradox and the following question came up:
Suppose the game doesn't end within nine rounds, then the player directly receives $2^{10}$ dollars , while ...
- 12.3k
4
votes
1
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279
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Is there a name for this probabilistic paradox?
Let $X\sim Exp(1)$ and $Y\sim Exp(\lambda)$, independent. Then,
\begin{align}
f_{X|Y=mX}(x) = \frac{f_{X,Y}(x,mx) }{\int f_{X,Y}(x,mx) \:dx }=\frac{f_X(x)f_Y(mx) }{\int f_X(x)f_Y(mx) \:dx } = \frac{e^{...
30
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7
answers
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Card doubling paradox
Suppose there are two face down cards each with a positive real number and with one twice the other. Each card has value equal to its number. You are given one of the cards (with value $x$) and after ...
- 1
2
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1
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115
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A Subjective Probability Paradox When Drawing Balls From an Urn
Suppose that you are randomly drawing balls from an urn without replacement. The urn contains an unknown number of white balls and exactly one black ball. Before starting to draw, your subjective ...
- 159k
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how does Bertrand's paradox challenge the classical definition of probability?
On page 9 of Papoulis's book[Probability, Random Variables, and Stochastic Processes], the classical definition of probability is as follows:
The probability of an event equals the ratio of its ...
2
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1
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250
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A variation on the three prisoners problem
Three prisoners hear that one of them will be executed (the exact person who will be executed is determined upfront, and cannot be changed), while the other two will be released. Prisoner A asks the ...
- 46.1k
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1
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Monty Hall Problem with unknown probabilities
Does someone know a solution to the following generalization of the Monty Hall Problem:
The Problem: Assume you are on Let's Make a Deal and are presented with the regular dilemma of the Monty Hall ...
- 37.3k
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1
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Paradox in Theory of probability of transition to polar coordinates
Let there are two independent random variables $X$,$Y$ with normal distribution. Vector $(X, Y)$ can be considered as a random point on the plane. Let $R$ and $\phi$ polar coordinates of this point.
...
- 14.7k
2
votes
2
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Probability of picking a real number randomly
If we randomly pick a real number from the number line, the probability of picking a number (say x) is 0. This is true for all real numbers x and it makes sense to me why this must be true. But ...
- 2,993
3
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2
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Set of possibilities for Simpson paradox
Italy is playing the U.S.A. in a football World Cup match. A successful pass is when a player on one team kicks the ball to a player on their team and it is not intercepted by the opposition. Is it ...
- 21.9k
0
votes
0
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224
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Forex rate: Expected value paradox
Let us suppose at present
1 dollar = 1 euro
After 1 year
There is 50% chance that 1 dollar = .80 euro ...[1]
And there is 50 % chance that 1 dollar = 1.25 euro ...[2]
Therefore expected value ...
- 539
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1
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133
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Modified two envelope paradox
This problem is a variation on a two envelope paradox.
This time Alice and Bob play the game. Envelopes X and Y, when opened contain money. One envelope has n dollars and the other has 2*n dollars. ...
- 24.6k
6
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Expected value of the distance between 2 uniformly distributed points on circle
I have the following problem (related to Bertrand):
Given a circle of radius $a=1$. Choose 2 points randomly on the circle circumference.
Then connect these points using a line with length $b$. ...
- 1