SUBJECT EVALUATION REPORT

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.

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In most instances where inferential statistics are applied in hypothesis testing, population distributions are unknown. Problems in hypothesis testing related to the central limit theorem most often occur when the sample data apply to perceptions and subjective evaluations by individuals, as opposed to objective data. Contemporary Professional Work Involving Waveform Analysis Waveform analysis was applied to the measurement and correction of ultrasonic pulse distortion in the human breast. One purpose of this research was to define an accurate, non-invasive technique for the diagnosis of malignant breast disease. This research was an application of ultrasonic pulse-echo RF waveform analysis and selected pattern recognition methods. The advantage of using an RF waveform format lies in its ability to contain both amplitude and phase information. Pattern recognition techniques such as the Fisher linear discriminant were used to determine various algorithms for classifying a tissue area. Tissue features used to develop the discriminant function were derived from the RF signal and evaluated by their respective Probability Distribution Function (PDF) curves. Only features having a physical explanation to its distribution a

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