Physics Forums » Set Theory, Logic, Probability & Statistics
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Join experts in discussion on Set Theory, Logic, Probability, and Statistics topics. Get to know the fundamentals in Set theory, logic, and proofs. Find information on Probability and statistics and also find homework help in the Physics Forums. Discuss Ten Simple Rules for Effective Statistical Practice and how helpful is the probability theory.
Physics Forums » Set Theory, Logic, Probability & Statistics
3d ago
This set-theory theorem is very easy to prove:
(*) if A≈B & C≈D & A∩C=∅ & B∩D=∅ then A∪C≈B∪D
It seems intuitive that if one replaces the strong
A∩C=∅ & B∩D=∅
condition by the weaker
A∩C≈B∩D
the implication
(**) if A≈B & C≈D & A∩C≈B∪∩D then A∪C≈BD
still holds.
(**) does not seem to be much...
Read more ..read more
Physics Forums » Set Theory, Logic, Probability & Statistics
2w ago
Hi there,
It's well known that for two assertions A and B : A → B is equivalent to (nonA or B).
The only proof I know of this equivalence relies on the truth table, one just brute forces all the possible combinations of truth values and then notice they're the same every time with A → B and...
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Physics Forums » Set Theory, Logic, Probability & Statistics
2w ago
In Aubrey Clayton's book" Bernoulli's Fallacy" which documents the conflict between frequentists and Bayesian interpretations of probability, he describes a problem that was proposed in the 19th century that gives a counterintuitive result.
The Problem:
"Infer the state of a bag of 3 balls...
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Physics Forums » Set Theory, Logic, Probability & Statistics
3w ago
https://anxieties.com/self-help-resources/fear-of-flying/how-safe-is-flying/
"In fact, based on this incredible safety record, if you did fly every day of your life, probability indicates that it would take you nineteen thousand years before you would succumb to a fatal accident."
The...
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Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
Hi, my background isn't mathematics but I was wondering how this kind of problem might be approached.
They have asked if there was a knot somewhere in an infinitely long rope, would the knot ever be reached if you iterated through the length hand over hand?
How could I start to tackle this...
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Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
I need a citation for the following proposition: Assume a random vector ##X=(X_1, ..., X_n)^T## with iid components ##X_i## and mean 0, then the distribution of ##X## is only invariant with respect to orthogonal transformations, if the distribution of the ##X_i## is a normal distribution.
Thank...
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Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
Hi,
in the Karhunen–Loève theorem's statement the random variables in the expansion are given by $$Z_k = \int_a^b X_te_k(t) \: dt$$
##X_t## is a zero-mean square-integrable stochastic process defined over a probability space ##(\Omega, F, P)## and indexed over a closed and bounded interval...
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Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
Hello,
I understand that a dataset that involves time ##T## as a variable and other variables ##Variable1##, ##Variable2##, ##Variable3##, represents a multivariate time-series, i.e. we can plot each variable ##Variable1##, ##Variable2##, ##Variable3## vs time ##T##.
When dealing with regular...
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Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
This set-theory theorem is very easy to prove:
(*) if A≈B & C≈D & A∩C=∅ & B∩D=∅ then A∪C≈B∪D
It seems intuitive that if one replaces the strong
A∩C=∅ & B∩D=∅
condition by the weaker
A∩C≈B∩D
the implication
(**) if A≈B & C≈D & A∩C≈B∪∩D then A∪C≈BD
still holds.
(**) does not seem to be much...
Read more ..read more
Physics Forums » Set Theory, Logic, Probability & Statistics
1M ago
My students still reckon Lande’s 2 motivations for ‘unless’ = ‘if not’ (below) too abstract, formalistic! Thus I need a 3rd simpler, motivation with merely etymology. But I never studied linguistics! How do I
1. use these etymology quotations, to motivate ‘unless’ = ‘if not’?
2. teach...
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