Title: Four Fundamental Questions in Probability Theory and Statistics,
Abstract: This study has the purpose of addressing four questions that lie at the base
of the probability theory and statistics, and includes two main steps. As
first, we conduct the textual analysis of the most significant works written by
eminent probability theorists. The textual analysis turns out to be a rather
innovative method of study in this domain, and shows how the sampled writers,
no matter he is a frequentist or a subjectivist, share a similar approach. Each
author argues on the multifold aspects of probability then he establishes the
mathematical theory on the basis of his intellectual conclusions. It may be
said that mathematics ranks second. Hilbert foresees an approach far different
from that used by the sampled authors. He proposes to axiomatize the
probability calculus notably to describe the probability concepts using purely
mathematical criteria. In the second stage of the present research we address
the four issues of the probability theory and statistics following the
recommendations of Hilbert. Specifically, we use two theorems that prove how
the frequentist and the subjectivist models are not incompatible as many
believe. Probability has distinct meanings under different hypotheses, and in
turn classical statistics and Bayesian statistics are available for adoption in
different circumstances. Subsequently, these results are commented upon,
followed by our conclusions