All Questions
Tagged with applications probability
82
questions
64
votes
17
answers
16k
views
Is the Law of Large Numbers empirically proven?
Does this reflect the real world and what is the empirical evidence behind this?
Layman here so please avoid abstract math in your response.
The Law of Large Numbers states that the average of the ...
- 767
25
votes
5
answers
9k
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Why does the Elo rating system work?
The Elo rating system is used to rank players in games such as chess. I can find plenty of explanations online of how to compute someone's Elo rating, how to actually crunch the numbers in practice, ...
- 28k
12
votes
7
answers
6k
views
Applications of Probability Theory in pure mathematics
My (maybe wrong) impression is that while probability is widely used in science (for example, in statistical mechanics), it is rarely seen in pure mathematics. Which leads me to the question -
Are ...
11
votes
1
answer
732
views
What precisely is the Friendship Paradox (and is Wikipedia wrong?)
Friendship paradox is the somewhat well-known statement that "statistically speaking, your friends have more friends than you do".
To my mind, which is surely ignorant of any complexities of social ...
- 12.7k
10
votes
2
answers
1k
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Does variance do any good to gambling game makers?
People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers?
In another word, what is a pratical gambling game that involving some ...
- 8,382
9
votes
3
answers
16k
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Maximum possible variance
From this biology article, end of page 4, the author talks about a random variable which never takes value outside the range $[0,1]$ ($0$ and $1$ included in the range). He says that the maximum ...
- 1,615
9
votes
4
answers
1k
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An unexpected application of non-trivial combinatorics
PROBLEM STATEMENT
Given two finite sets $A$ and $B$, each containing $s \in \mathbb N$ elements, how many pairs of functions $f \colon A \rightarrow B$ and $g \colon B \rightarrow A$ are there, ...
- 365
8
votes
6
answers
9k
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Understanding Black-Scholes
Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage:
Black-Scholes
Many thanks.
- 83
6
votes
1
answer
2k
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Background for studying and understanding Stochastic differential equations
Assume I have back ground of the following knowledge based on the textbook as :
ODE : ODE by Tenenbaum
Baby probability : Ross 's baby probability
Baby real anlysis : Bartle's introduction to real ...
- 1,975
6
votes
1
answer
176
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Why do my Stack Exchange reps follow a power law?
I noticed a pattern while looking at my network profile the other day, and I'm wondering if it's a fluke, or if there is something deep to it.
My reps for my top five Stack Exchange communities ...
- 15.4k
5
votes
5
answers
763
views
Decoding Every Top 100 Voting Ever
I need expert help on the math behind the following voting mechanism, any comment towards solutions are greatly appreciated!
--
A country is holding a poll to determine the top 100 restaurants out ...
- 51
5
votes
1
answer
105
views
Math of Jury Sizes
If we go by the assumption that a Jury is a representation of the public at large, then is 12 people statistically signficant?
When doing any scientific survey or poll, a sample of 12 people would be ...
- 4,425
4
votes
3
answers
5k
views
Probability of 15 consecutive green lights
Introduction
Upon a trip home, my mother and I were noticing a very peculiar occurrence: Traffic lights were almost continuously green. Indeed, exactly fifteen different traffic lights were green ...
- 5,760
4
votes
2
answers
2k
views
Biology: Wright-Fisher model of genetic drift
In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
- 1,615
4
votes
1
answer
60
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Approximative formula for normal distribution being above threshold
Suppose that $X \sim \mathcal{N}(r + \frac{1}{N}, s) $ and $Y \sim \mathcal{N}(r, s)$ for some $r, s \approx 1$ and $N \approx 10^6$.
What are good approximate formulas for the quantity
$$\frac{ \...
