Đề thi giữa học kì 3 môn Xác suất thống kê năm 2024-2025

This document presents a comprehensive midterm examination designed for the "Probability and Statistics" course (MT2013) at the Faculty of Applied Sciences, Ho Chi Minh City University of Technology. In the realm of scientific and engineering disciplines, a robust understanding of xác suất và thống kê is paramount for data-driven decision-making, process optimization, and risk assessment. This examination serves as a critical assessment tool, aiming to evaluate students' foundational knowledge and their ability to apply core statistical principles to practical scenarios. It covers essential concepts ranging from properties of biến ngẫu nhiên to the practical application of various phân phối xác suất, thereby highlighting the importance of quantitative reasoning in complex systems.

University students pursuing degrees in applied sciences, engineering, or related quantitative fields, enrolled in an introductory to intermediate course on Probability and Statistics. Also relevant for educators developing statistical assessments.

This midterm examination for the "Probability and Statistics" course systematically assesses students' analytical and problem-solving skills across a spectrum of advanced statistical topics. Comprising 16 multiple-choice questions, the exam meticulously evaluates comprehension of concepts such as the fundamental properties of biến ngẫu nhiên, including their kỳ vọng and phương sai. A significant portion addresses the analysis of độ tin cậy hệ thống, exemplified by signal processing modules, requiring the calculation of xác suất for successful system operation. Furthermore, the exam delves into various phân phối xác suất, focusing on continuous random variables through the interpretation and application of hàm phân phối tích lũy (CDF) to determine unknown parameters, calculate probabilities for specific intervals, and analyze transformations. Discrete random variables are explored within the practical context of kiểm soát chất lượng, involving the assessment of defective items in product batches and related sampling probabilities. The module also covers scenarios related to thời gian chờ, implicitly testing knowledge of the phân phối mũ and its applications. Each question is aligned with specific learning objectives (L.O.1, L.O.2), ensuring a thorough evaluation of theoretical understanding and practical application. The assessment format, which includes a penalty for incorrect answers, promotes precision and critical thinking. The comprehensive nature of this exam underscores the practical value of statistical methodologies in solving real-world challenges, from engineering design to business analytics.