Related papers: The two envelopes probability paradox: Much ado ab…
The problems of conditional entropy's definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented. Examples are given to prove the conclusion that…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
The analysis of the arguments within the limits of the classical thermodynamics that lead to the Gibbs paradox was made. Features of preconditions used in the derivation of the entropy of mixing of ideal gases that caused the appearance of…
We generalize the quantum "pigeonhole paradox" to quantum paradoxes involving arbitrary types of particle relations, including orderings, functions and graphs.
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
We show in this note that Gibbs paradox arises not due to application of thermodynamic principles, whether classical or statistical or even quantum mechanical, but due to incorrect application of mathematics to the process of mixing of…
In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice,…
We study an ensemble of individuals playing the two games of the so-called Parrondo paradox. In our study, players are allowed to choose the game to be played by the whole ensemble in each turn. The choice cannot conform to the preferences…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.
In this note our aim is to show a paradox in the spectral representation of stationary random processes.
We present a novel paradox in special relativity together with its solution. We call it the four particles paradox. The purpose of this paradox is pedagogical and therefore directed towards students and lecturers of physics. Even if most…
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…