### Most Probable Questions for Mathematics-IIA (BS-M201) Exam Based on the syllabus and previous year questions (PYQs), here are the highly probable questions categorized by modules, along with important topics and chapter-wise weightage. --- ## Module-wise Important Topics & Probable Questions ### Module 1: Basic Probability (11 lectures) - Weightage: ~20-25 marks - Key Topics: - Conditional probability & Bayes’ Theorem (Repeated) - Discrete random variables (Binomial, Poisson) (Repeated) - Expectation, Variance, Chebyshev’s Inequality - Probable Questions: - Bayes’ Theorem: A factory produces defective bolts (PYQ 2023). - Binomial Distribution: Find mean/variance (PYQ 2019, 2023). - Poisson Approximation: Probability of events (e.g., bank customers per hour) (Repeated). --- ### Module 2: Continuous Probability Distributions (4 lectures) - Weightage: ~10 marks - Key Topics: - Exponential & Normal distributions (Repeated) - PDF/CDF calculations - Probable Questions: - Exponential Distribution: Shower duration problem (PYQ 2019). - Normal Distribution: Find \( P(X > a) \) or percentage of defective items (PYQ 2023, 2024). --- ### Module 3: Bivariate Distributions (5 lectures) - Weightage:~10-15 marks - Key Topics: - Joint PDF, Marginal/Conditional distributions (Repeated) - Covariance & Correlation (Repeated) - Probable Questions: - Joint PDF: Find constant \( C \) and \( P(X < a, Y > b) \) (PYQ 2019). - Correlation: Prove \( \rho_{XY} = -1 \) for linear relations (PYQ 2019). --- ### Module 4: Basic Statistics (8 lectures) - Weightage: ~15 marks - Key Topics: - Measures of central tendency & dispersion (Repeated) - Binomial/Poisson/Normal distributions (Repeated) - Rank Correlation (Repeated) - Probable Questions: - Rank Correlation: Correct calculation after data error (PYQ 2023). - Skewness/Kurtosis: Interpret values (PYQ 2024). --- ### Module 5: Applied Statistics (8 lectures) - Weightage: ~15-20 marks - Key Topics: - Curve fitting (Least Squares) (Repeated) - Large sample tests (Proportion, Mean) (Repeated) - Probable Questions: - Least Squares: Fit straight line/parabola (PYQ 2019, 2023, 2024). - Z-test : Compare population means/proportions (PYQ 2023, 2024). --- ### Module 6: Small Samples & Chi-square Tests (4 lectures) - Weightage: ~10 marks - Key Topics: - t-test, F-test, Chi-square test (Repeated) - Goodness of fit & Independence of attributes - Probable Questions: - Chi-square Test: Check birth gender consistency (PYQ 2019). - t-test: Compare sample means (PYQ 2024). --- ## Final Suggestions 1. Most Repeated Topics: - Probability: Bayes’ Theorem, Binomial/Poisson. - Statistics: Least squares, Normal distribution, Z-test. - Correlation: Rank correlation, Joint distributions. 2. High-Weightage Modules: - Basic Probability (25%) - Applied Statistics (25%) - Continuous Distributions (15%) 3. Must-Practice Problems: - Numericals: - Bayes’ Theorem (Machine defect problem). - Least squares fitting (Straight line/parabola). - Normal distribution \( P(X > a) \) calculations. - **Derivations**: - Variance of \( X + Y \) (PYQ 2023). - Gibbs-Helmholtz equation (PYQ 2019). 4. PYQ Patterns: - Short Answers: Definitions (e.g., Kurtosis, Type I error). - Long Answers: Hypothesis testing (Z/t/Chi-square tests). --- ### Conclusion - Focus more on Modules 1, 4, and 5 (highest weightage). - Revise PYQs (many questions are repeated verbatim). - Practice numericals (Probability, Curve fitting, Hypothesis testing). Good luck! 📊 By - FUTURE MINDS