Beta, Weibull, Pareto and Cauchy Distribution with properties. Inversion theorem. Central limit theorem. Law of large numbers. Bivariate distribution, Marginal distribution, Conditional distribution and independence, Conditional expectation and conditional variance, Bivariate Normal Distribution and its properties. Transformation of variables of discrete and continuous types. Expectations of functions of random variables. Sum, product and quotient of random variables. Cumulative distribution function and moment generating function techniques. Derivations of Chi-square, t and F distributions and their properties. Distribution of the rth order statistics. Distribution of sample range, sample median and sample mid-range.

To discuss the concept of joint and conditional distributions, Stochastic Independence, Distributions of Functions of Random Variables, Order statistics and Sampling Distributions.

Students should be able to discuss the properties of probability distributions as well as sampling distributions. They should also be able to deal with Ordered Statistics.

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Book Title : Introduction to the Theory of Statistics

Author : Mood, A.M., Graybill, F.A. and Boes, D.C.

Edition : 3rd

Publisher : McGraw-Hill Book Company

Book Title : Introduction to Mathematical Statistics

Author : 2. Hogg, R.V. and Craig, A.T.

Edition : Fifth Edition

Publisher : Prentice-Hall International, Inc. Engle Wood Cliffs, N.T.

Book Title : A Course in Mathematical Statistics

Author : Hirai, A. S. (1998)

Edition :

Publisher : Ilmi Kitab Khana, Lahore.

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