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Annexure ‘AAB-CD-01’ Course Title: PROBABILITY THEORY – I Course Code: to be decided later Credit Units: 4 Level: UG # L T 3 1 P/ S Course Title Course Objectives: The objective of the course is to develop knowledge of the fundamentals of the probability theory for determining the risk and assessing the various problems based on it. The application of this theory in various decision making problems especially under uncertainties. 2 Prerequisites: NIL 3 Student Learning Outcomes: The students will be able to distinguish between probability models appropriate to different chance events and calculate probability according to these methods. The students will learn to get the solution of the problems based on probability space and limit theorems. The students will learn to get the solution of the problems based on random variables and distribution functions. The students will learn to get the solution of the problems based on mgf and cf for discrete and continuous distributions. The course enables the students to develop the skill set to solve probability based real life problems. Course Contents / Syllabus: 4 Module I: SW/F W 0 Weighta ge (%) 1 5 Random experiment, trial, sample point and sample space, events, operations of events, concepts of equally likely, mutually exclusive and exhaustive events. Definition of probability: Classical, relative frequency and axiomatic approaches. Discrete probability space, properties of probability under set theoretic approach. Independence of events, Conditional probability, total and compound probability theorems, Bayes theorem and its applications. Module II: 6 Random variables – discrete and continuous, probability mass function (pmf) and probability density function (pdf), Cumulative distribution function (cdf). Joint distribution of two random variables, marginal and conditional distributions. Module III: 7 Independence of random variables. Expectation of a random variable (rv) and its properties, expectation of sum of random variables and product of independent random variables, conditional expectation and related problems. Module IV: 25% Weighta ge 25% Weighta ge 25% Weighta ge 25 TOTAL CREDIT UNITS 4 Weighta ge 8 9 Moments, moment generating function (m.g.f.) & their properties, continuity theorem for m.g.f. (without proof).Chebyshev’s inequality. Complements and problems. Pedagogy for Course Delivery: The class will be taught using theory and practical methods using software in a separate Lab sessions. In addition to numerical applications, the real life problems and situations will be assigned to the students and they are encouraged to get a feasible solution that could deliver meaningful and acceptable solutions by the end users. Assessment/ Examination Scheme: Theory L/T (%) Lab/Practical/Studio (%) End Term Examination 30% NA Theory Assessment (L&T): Continuous Assessment/Internal Assessment Components (Drop down) 70% End Term Examination MidTerm Exam Project Viva Attendance 10% 10% 5% 5% Weightage (%) 70% Text & References: 1. Parzen, E.S. : Modern Probability Theory and its Applications. 2. Meyer, P. : Introductory Probability and Statistical Applications. 3. Stirzekar David (1994) : Elementry Probabilityu, Cambridge University Press. 4. Mood A.M., Graybill F.A. and Boes D.C. (1974) : Introduction to the theory of Statistics, McGraw Hill. 5. Mukhopadhyay, P : Mathmatical Statistics, new central book agency. 6. Hoel, P. G., Port, S. C. and Stone, C. J, Introduction to Probability Theory, Universal Book Stall, New Delhi, Reprint 2003. 7. Chung, K. L., A Course in Probability Theory, Academic Press, San Diego, USA, 2001 Remarks and Suggestions: _______________________________ Date: Name, Designation, Organisation