The paper presents the university course Theory of Probability and Mathematical Statistics created on the electronic platform MOODLE at Trade Co-operative University of Moldova (TCUM) for distance learning. This e-course is presented in three sections: Random events; Random variables; Elements of Mathematical Statistics. Topics include a brief summary of the theory (Lecture Notes LN). Subsequently the exposed Lecture Notes are accompanied by multiple problems and worked examples with explanations (Exercises Solved - ES). All themes end with a series of problems to be solved (Suggested Exercises - SE). The answers to all outstanding issues (Answers - A) and tables needed to solve some of them are provided in the latter part of the paper. Self-Assessment Tests are provided at the end of each topic and are structured in three levels of learning the material studied: knowledge, implementation and integration. The Base of Questions has the same structure as the SelfAssessment Tests, and it also oversees the completion and operational processing of its contents. A Summative Evaluation of Knowledge Tests is provided at the end of each compartment. Finally, consulting the connections, readers will find many other titles of books and electronic sources that will effectively serve to strengthen and deepen the knowledge acquired from studying this course. In the Questionnaire option, users have the opportunity to express their opinions on the usefulness and effectiveness of this instrument and the means of training and learning the proposed course, which is always welcome and expected by the authors of the opposite present.