All Questions
Tagged with applications probability
82
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Probability that random variables with multinomial distribution have a common divisor greater than 1
Consider an election in which $k$ candidates compete: Let $N_{i}$ denote the number of votes for candidate $i$ in the election.
How can we reasonably estimate the probability that the number of votes ...
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1
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Standard definition of a game in game theory
Sorry for my naive question, but at the moment I can't quite figure it out.
I'm consulting various documents on game theory in order to get the standard definition of what a game (and an associated ...
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Formula like Elo rating but for games where the outcome is numeric?
I'm working on a problem that involves ranking based on pairwise comparisons (it's for a scientific problem, not actually for games). My comparisons return a numerical score (in practice roughly ...
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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 ...
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Probability analysis in passengers taking trains in a FCFS way under capacity constraint
Suppose there are two trains:
Train 1 and Train 2 have different departure times ($t_1$ and $t_2$) and capacities ($c_1$ and $c_2$).
There are two types of passengers, Type 1 with $d_1$ passengers ...
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A "perfect" (chess) rating system
Assume we want to have a player rating system with the following conditions:
For simplicity, no draws.
If A wins against B with ratings $a,b$, their new ratings are $a'=f(a,b),b'=g(a,b)$.
Most ...
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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, ...
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How to develop an algorithm to prioritize set members based on various criteria
I tried looking for responses and Google. It has been a while since I used math to any capacity and the lack of application is only surpassed by my inability to articulate the concepts. That's my long-...
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Exercise 1-28 A high school lottery uses two sets of numbered balls...
Exercise 1-28
A high school lottery uses two sets of numbered balls. One set consists of ten white balls numbered 1-10 and the second set contains twenty blue balls numbered
1-20. To play, you select ...
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Is measure theory only for integrals?
I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue ...
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Is below an example of Bayes theorem?
I went to an institute for hiring with low gender diversity (1 female students out of 10 male students), and observed an application of bayes theorem. Can you please confirm if is TRUE/ my thinking is ...
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What is the probability that a marble from the urn has been picked up by exactly $n$ people?
An urn starts with $m$ marbles and is then approached by $p$ people, each of which picks up $k$ marbles, discarding one and returning the rest to the urn. The urn now has $m - p$ marbles remaining. ...
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Assessing the efficiency of a single vote in a multiparty presidential election
In a country there is a voting system where all parties get represented in parliament if they meet a bar of $n$ percent.
Suppose that the parties are grouped into two groups of red $R_1, \dots R_k $ ...
- 1,125
4
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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{ \...
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Is one SAT guessing strategy better than another?
The context is this paragraph from my SAT & ACT Prep book on page 11.
"There is one thing to keep in mind: Pick one letter for the SAT or a two-letter combo for the ACT and stick to it ...
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