All Questions
Tagged with philosophy probability-theory
23
questions
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43
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Why do the increasing sequences $x_n, y_n$, decrease to $x,y$ to show a bivariate (or univariate) cdf is right continuous?
I have a problem understanding why the concept of right continuity of a cdf has to decrease a sequence $x_n$ or $y_n$ to a limiting value $x$ or $y$ respectively.
I do not understand why in this ...
- 313
1
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1
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56
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Conditioning in Event Language VS Proposition Language
According to this video, one can freely decide to conceptualize probabilities in terms of either event language or proposition language. It states, "the mathematical rules are applied the same ...
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2
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189
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The correct physical interpretation of Binomial distribution and bernoulli trial in this example
We know that every random variable can have a probability distribution. Examples include the number of heads in many tosses, or the number of ones on a dice after many rolls and so on.
Suppose we use ...
- 203
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2
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84
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What is the fundamental difference between choosing a ball and rolling a die type of problems in probability?
Suppose, I have a box where I have $n$ balls out of which $b$ are blue. Hence, the probability of picking up a blue ball at random is $p=\frac{b}{n}$.
Now suppose, I know the total number of balls, ...
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How are outcomes generated in a probability space?
Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a probability space.
This (somewhat philosophical) question concerns the sample space, $\Omega$, or rather the outcomes $\omega \in \Omega$. Commonly, the $\...
- 349
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Is there a mathematical basis for the idea that this interpretation of confidence intervals is incorrect, or is it just frequentist philosophy?
Suppose the mean time it takes all workers in a particular city to get to work is estimated as $21$. A $95\%$ confident interval is calculated to be $(18.3, 23.7).$
According to this website, the ...
- 68.1k
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Increase in conditional probability for contradictory hypotheses in bayesian confirmation theory?
Although this question has a philosophical slant and my motivations for asking it are philosophical, I'm going to justify asking this in the mathematics stack exchange in two ways:
1) I've asked ...
- 126
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3
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359
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Good resources on the intersection of probability theory and logic from a foundations/philosophical perspective?
What are some good books, courses, or online resources for probability theory that highlights differences between classical, frequentist, Bayesian, epistemic etc.? I majored in philosophy and am now ...
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Expected Value Of A Process - Formalization / Foundations
Consider the question: Let $X$ be the random variable describing the number of rolls of a six-sided die needed till you see a $6$. What is $\mathbb{E}(X)$? Usually the answer given is $6$. What is ...
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Landscape of probability theory [closed]
I'm an engineering student who has taken one undergraduate course in probability theory, but that's all my exposure so far. I'm trying to get into machine learning and need to develop more of a ...
- 690
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Can there be a lottery of the natural numbers? [duplicate]
Can there be a lottery of the natural numbers, so that every natural number is chosen equally likely?
The standard answer would be "No" because: If we define a measure $\mathbf{P}$ on $\mathbb{N}$ so ...
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28
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3
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10k
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Probability and measure theory
I'd like to have a correct general understanding of the importance of measure theory in probability theory. For now, it seems like mathematicians work with the notion of probability measure and prove ...
- 2,113
3
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1
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178
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Troubling questions about probability
Suppose we have some random phenomena. Is it true that any event concerning the phenomena has a fixed "correct" probability? That is, the correct probability is the relative number of occurrences of ...
- 1,353
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3
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Why does randomness exhibit a pattern in the long run?
!!! Layman here so please avoid complex math and answers.
Random (usually pseudorandom) events are usually characterized along these lines:
Each outcome in a trial experiment must be i.i.d.; i.e. it ...
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Do the Kolmogorov's axioms permit speaking of frequencies of occurence in any meaningful sense?
It is frequently stated (in textbooks, on Wikipedia) that the "Law of large numbers" in mathematical probability theory is a statement about relative frequencies of occurrence of an event in a finite ...
