The overall aim of the course is to give a good understanding of · Complex Numbers, variables and functions (revision). · Cauchy-Riemann equations, complex integrals, power series and its convergence.· Cauchy’s theorem and integrals formula, Taylor’s theorem and Laurent expansion, Residues and Jordan’s theorems, evaluating (improper) real integrals.· Integrals transforms of Laplace, Fourier, Mellin, Complex Fourier and their inversion integrals.· Generating and characteristic Functions, complex approach to obtain the distribution of sum, differenceand product of continuous independent random variables.

: The main purposesof this course are: · Making an individual understanding to the basic theoretical knowledge aboutfundamental principles of the estimation theory and its techniques. · To identify a good estimator. · To learn the concept of the Uniformly Minimum Variance Unbiased Estimators (UMVUE). · To establish various properties of likelihood estimators. · Understanding the concept of statistical estimation under Bayesian framework.

· The concept of Bayesian decision making , Expected loss and decision rules (nonrandomized and randomized). · The Decision principles (conditional Bayes, frequents), inference as decision problem and optimal decision rules. · The Bayes and minimax decision rule and admissibility of minimax. Conjugate prior families and hierarchical priors. · The Parametric Empirical Bayes, Posterior distribution, Loss function and squared error loss. The precautionary loss and LINEX loss and Bayes HPD confidence intervals

· Theconstruction of Most Powerful (MP) tests and UniformlyMost Powerful (UMP) tests. · IdentifyingtheUniformly Most Powerful Unbiased (UMPU) tests and Locally best tests. · The obtaining of the power and power function of the test. · The concept of Generalized Likelihood Ratio Test (GLRT) and Sequential Probability Ratio Test (SPRT) . · Uniformly most accurate one-sided confidence Interval and its relation to UMP tests for one-sided null against one-sided alternative hypotheses. The construction of shortest expected length confidence interval.

· To introduce the concept of a time series, and discuss a range of descriptive methods for identifying features of interest; · To present a range of approaches for representing trends and seasonality in a time series, and to assess their relative merits; · To describe the theoretical properties of commonly used time series models; · To describe a range of approaches for predicting future values of a time series;To show how to apply the techniques from the course to real time series data sets in the statistical package R.

1- To introduce branch which is an integration of mathematics, statistics, and economics used to deal with econometric models. 2- To provide the students with some useful tools for his/her future research. 3- . To help the student to develop a way of thinking in quantitative terms. 4- To help the students understanding simultaneous Equation Models

· To provide an understanding of the basic concepts in probability theory · Characteristic functions and their properties · Types of convergence and the limit of probability distributions.