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INDIAN INSTITUTE OF TECHNOLOGY RAJASTHAN (SUMMER TERM 2013-14) Course Number : 22001 Course Title : Probability & Statistics Instructor : Dr. Gaurav Bhatnagar UNIT 1: INTRODUCTION TO PROBABILITY Definitions, sample, space & events, joint & conditional probability, dependent events. Elementary theory of probability, Baye’s theorem with simple applications, Expected value. UNIT 2: RANDOM VARIABLES Introduction, distribution & density functions, discrete & continuous random variables, special distributions: binominal, poisson, uniform, exponential, normal, rayleigh. Central limit theorem. UNIT 3: EXPECTATION, CONDITIONAL DISTRIBUTION AND CONDITIONAL EXPECTATION Random variable, Expectation of random variable, joint distribution functions, joint probability density function, conditional distribution & density functions, Conditional Expectation. Mean & variance, chebyshev’s inequality, characteristic functions & moment generating function, covariance & correlation coefficient of multiple random variables. UNIT 4: REGRESSION, CORRELATION AND STATISTICAL INFERENCE Introduction, Least-square curve fitting, multiple regression, Correlation Analysis, method of maximum likelihood estimation, point estimation, Estimation of variance, Hypothesis testing. Text Books: Sheldon M. Ross, Introduction to probability and statistics for engineers and scientists, Elsevier. Vijay K. Rohatgi and A. K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics, Wiley. Kai L. Chung and F. Aitsahlia, Elementary Probability Theory, Springer. Reference Books: Robert V. Hogg, Allen T. Craig and Joeseph W. McKean, Introduction to Mathematical Statistics, Pearson. William Feller, Introduction to Probability theory and its applications, Wiley. Richard A. Johnson, Miller and Freund’s Probability and Statistics for Engineers, PHI Learning. T.T. Soong, Fundamentals of Probability and Statistics for Engineers, Wiley. Evaluation Plan: S.No. 1. 2. 3. 4. Title Quiz/Attendance First Mid-term Second Mid-term End Exam Weightage 20% 20% 20% 40% Note: No makeup exams for quizzes and mid-term exams. However, the end exam will be considered only after submitting the proper documentation.