All Questions
Tagged with applications probability
82
questions
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Election Toy Model leads to a question of an interesting function if it exists
In Canada there is an election going on and I was pondering about a function in which you have the polling averages for the different parties $x_1, x_2, x_3... x_n$ and then a function $f(x_1), f(x_2)....
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Empirical application for probability of $h$-deranged permutations
Background
For $n \in \mathbb{N}$ distinct items, there are a total of $n!$ permutations of them. A derangement is a permutation in which not a single item is in its 'natural position'. The number of ...
- 1,876
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What is the use of the theorem on expection on a function of a random variable?
If $X$ is a random variable, then the expectation of $X$ is defined as
$$E[X] = \sum_{x} x p_{X}(x)$$
Where $p_X$ is a pmf on $X$.
If $g$ is a real valued function then I learn the following theorem
$$...
- 2,365
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1
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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
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1
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46
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Time needed to check all possible combinations
Suppose we want to find the time needed to write down all possible combinations of 58 characters.
With a string of size n the possible combinations are 58^n.
We pick random characters every time we ...
- 35
3
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1
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257
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Real-world application where strong LLN is needed (weak LLN is not enough) [closed]
Do you know of any real world (algorithm, physics, ...) application of the law of large numbers where we need the strong LLN and the weak LLN by itself is not enough to prove that the application is ...
- 785
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45
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The law of large numbers
I'm currently writing a dissertation on the law of large numbers. The 4th chapter is on the real-life applications of the laws themselves. I have found applications for the laws in general but would ...
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Primer for mathematical models of epidemics
In a comment to my recent MO question Robert Israel wrote: "Mathematical models of epidemics are well-established. Of course we'd like to know the parameters (and to what extent something can be done ...
- 1,133
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2
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How can I understand Wasserstein Metric?
I've met Wasserstein metric in different topic, most in sampling and mathematic model of machine learning.
For two density function $\mu,\nu$ on $R^d$, the wasserstein distance between $\mu,\nu$ can ...
- 507
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127
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Max Distance of a Simple Random Walk on Integers
I encounter this when proving bounds for a randomized algorithm, which is mathematically formulated below. Many thanks for any thoughts or discussions given.
Consider simple random walk $S_n = X_1 + \...
- 98
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46
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Probability someone never gets promoted?
I was doing some simulations on societal structures. For example, given a population, with a heirachy of N levels. e.g. one prime-minister, 10 cabinet members, 100 MPs, and so on. Let $P$ be the ...
- 4,425
5
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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
5
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5
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763
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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
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532
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How to convert an instantaneous mortality rate to a weekly mortality rate
I want to convert an instantaneous mortality rate that is reported per year (actual value = $0.58y^{-1}$) into a weekly mortality rate.
This answer gives the formula as $j=(1+i)^{1/12}-1$ where $j$ ...
- 223
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Probability of stripes being distinguishable given probability density functions for each luminance
I have an image with seven stripes on it (or three stripes on a dark background), and the goal is to estimate the probability of whether they are distinguishable from one another.
If the values of ...
- 3,212