The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Introduction.- Normal Distributions.- Student's Distributions.- Sum, Product & Ratio for the Normal Random Variables.- Sum, Product & Ratio for the Student's Random Variables.- Sum, Product & Ratio for the Normal and Student's Random Variables.- Product of the Normal and Student's Densities.- Characterizations of Normal Distributions.- Characterizations of Student's Distributions.- Concluding Remarks.