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SYLLABUS

                                                           Statistics

              Objectives:
                  To understand the value of Statistics in acquiring knowledge and making decisions in today's society.
                  To  learn about the basic theory of  Probability, random variable, moments generating function, Probability distribution, reliability
                   theory, laws of large numbers, correlation and regression, sampling theory, theory of estimation and testing of hypotheses.

                     Sr. No.                                      Content

                        1      The sample space, Events, Basic notions of probability, Methods of enumeration

                               of Probability, conditional probability and independence, Baye’s theorem

                        2      General notion of a variable, Discrete random variables, Continuous random
                               variables, Functions of random Variables, Two dimensional random variables,

                               Marginal and conditional probability distributions, Independent random
                               variables, Distribution of product and quotient of independent random variables,

                               n-dimensional random variables

                        3      Expected value of a random variable, Expectation of a function of a random
                               variable, Properties of expected value,

                                Variance of a random variable and their properties, Approximate expressions for
                               expectations and variance, Chebyshev inequality

                        4      The Moment Generating Function: Examples of moment generating functions,

                               Properties of moment generating function, Reproductive properties, Discrete
                               Distributions : Binomial, Poison, Geometric, Pascal Distributions, Continuous

                               Distributions :Uniform, Normal, Exponential

                        5      Basic concepts, The normal failure law, The exponential failure law, Weibul
                               failure law, Reliability of systems

                        6      Weak Law of Large Numbers, Strong Law of Large Number, Central Limit
                               Theorem, Confidence Intervals

                        7      The correlation coefficient, Conditional expectation, Regression of the mean

                        8      Samples, Sample Statistics, Sampling Distribution of Sample Mean and Sample
                               Variance, t-distribution , Chi Square distribution, F- distribution

                        9      Estimation of Parameters: Criteria for estimates, Maximum likelihood estimates,
                               Method of least squares

                       10      t-test, chi square Godness of fit, Z-test with examples
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