SUBJECT EVALUATION REPORT: PROBABILITY, RANDOM VARIABLES, AND RANDOM SIGNAL PRINCIPLES
This research develops a subject evaluation report on probability, random variables, and random signal principles. The approach to this subject evaluation is to use concepts and principles presented by Peyton Peebles in Probability, Random Variables, and Random Signal Principles to analyze and describe contemporary professional work in this field. A random signal is a waveform; thus, the analysis and description of contemporary professional work in this field emphasizes waveform analysis. The concept of probability and the application of Bayes' Theorem are prominent in waveform analysis. Therefore, these conceptual issues are addressed in this subject evaluation prior to analyzing contemporary professional work in waveform analysis.
Probability is "a number expressing the likelihood of occurrence of a specific event." For use in inferential statistics, this probability must be statistically independent.
One means of improving probability estimates is the application of Bayes' Theorem. Classical statistics are concerned with the analysis of sampled data. The analysis of sampled data permits the researcher to make inferences concerning total populations, with the exclusion of any personal judgment or opinions. To the contrary, Bayesian statistics purposefully incorporates informed judgments into the analyses of data.
Bayesian statistics are based on Bayes' theorem, which is concerned with the derivation of a conditional probability--an alteration of the probability found through the application of classical statistical analysis. Bayes' theorem is a variation on the general formula for conditional probability. The significance of Bayes' theorem is that it is applied in the context of sequential events, and further, that the computational version of the formula provides the basis for determining the conditional probability o...