Discussing properties of the autocorrelation function.
a) State Bayes’ theorem. b) Define MGF of a random variable. c) Give the memoryless property of exponential distribution. d) What is a wide-sense stationary (WSS) process? e) Write the relation between autocorrelation and PSD. f) Find the mean and variance of a Binomial random variable with parameters (n, p). probability theory and random processes dbatu question paper
Calculating the Karl Pearson’s coefficient of correlation and obtaining regression equations. Discussing properties of the autocorrelation function
| Section | Question Type | Marks per Question | Topics Frequently Asked | | :--- | :--- | :--- | :--- | | | Short Answers / Objective | 2 to 3 Marks | Axioms of prob, PDF vs PMF, Autocorrelation properties, Stationarity types. | | A (Q2) | Long Answer (Numerical) | 7 to 8 Marks | Bayes Theorem, Poisson Distribution, Exponential distribution. | | A (Q3) | Long Answer (Derivation) | 7 to 8 Marks | Central Limit Theorem (Statement), MGF for Binomial/Normal, Regression lines. | | B (Q4) | Long Answer (Numerical) | 7 to 8 Marks | Joint PDFs, Marginal densities, Correlation coefficient. | | B (Q5) | Long Answer (Derivation) | 13 Marks | The big one : WSS process properties, Wiener-Khinchin, PSD of RC circuit noise. | | B (Q6) | Long Answer (Mixed) | 7 to 8 Marks | Poisson process (Arrival times), Random Walk probability. | c) Give the memoryless property of exponential distribution
| Particulars | Details | |--------------|---------| | | 60 Marks (End Sem) + 40 Marks (Internal: 20 CIA + 20 MSE) | | Time Duration | 3 Hours | | Total Questions | 6 to 8 questions, answer any 4 or 5 (as per DBATU pattern) | | Question Nature | Mix of theory, derivations, numerical problems, and proofs | | Unit Distribution | Typically one question per unit (Unit 1 to Unit 6) |
When analyzing a certain patterns emerge. The examiners at DBATU follow a structured pattern, usually split into two sections: Section A (short answers) and Section B (descriptive/numerical).
