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Descriptive of Compulsory Statistics Courses

ST101 : General Statistics I CREDITS 3

General concepts, Concept of statistics and its relation ship to other science.
Statistical data and methods of collecting data.
Frequency distribution, Cumulative frequency dist.
Geometrical representation of data.(graphical)
Measures of central tendency (Mean, Mode, Median, geometric mean, harmonic mean percentiles.)
Measures of dispersion (range, mean deviation, variance, standard deviation, standard error of the mean pooled variance).
Properties of (Variance, Coefficient of variation, Standard Scores, Moments, Skew ness, Kurtosis).
Simple regression and correlation (fundamental idea).
Concept of probability (fundamental idea).
Binomial distribution.
Normal distribution.

ST201 : General Statistics II CREDITS 4 •

General review of (ST101), Sampling distribution of the sample mean. General concepts and properties of Chi-squarer, Student-t, Snedecor-F distribution, relationship between t and F, population parameters. Concept of interval estimation, Confidence limits for single mean, difference between two means, single proportion, difference between two proportions.

Correlation: general concepts, simple, partial, multiple correlation coefficient. Test and confidence limits concerning simple correlation.

Spearman’s rank correlation coefficient, contingency and association coefficients. Chi-square test for independency and association contingency tables. Regression: general Concepts, linear regression (with no more than two independent variables), estimation, test and confidence limits concerning regression parameters.

ST202 : Probability I CREDITS 3 •

Counting methods (basic counting method, permutations, combinations, (with replacement and without replacement)).

Random experiment.
Probability theory (definitions, axioms and theorems).
Conditional Probability

Laws of probability.(Addition & Multiplication law)

Bayes theorem.
Random variables (definitions).
Probability Mass Function. & Probability Density Function
Distribution function.
Properties of random variable (expectation and its properties, variance and its properties, moments and moment generating function, probability generating function).
Simple idea about Chebyshev’s Inequalities.
Simple idea about Binomial, Poisson, Normal dist.

ST301 : Probability II CREDITS 4 •

Introduction (a simple review of ST202).

Probability generating function.
Characteristic function.
Some measures about distributions ( mode, median, mean, variance, skew ness, kurtosis)
Some parametric families of discrete distributions and their properties: (Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Hyper Geometric).
Some parametric families of continuous distributions ( Uniform, Normal, Log-Normal, Gamma, Exponential, Beta)
Joint, marginal and conditional distributions.
Conditional expectations, covariance, conditional variance Multinomial dist.

ST302 : Statistical Method I CREDITS 4 •

Introduction, samples: sample and population, statistics and parameter, mean, variance and standard error of a sample, estimator of population variance, pooled variance.

Linear combinations of random variables. Calculating the mean and variance of a linear combination.
Sampling from Normal Population, the distribution of linear combination. of normal dist.
The mean and variance of a sample.
Test of Hypothesis : Null and Alternative hypothesis, critical region, type I & type II error, level of significance, degree of freedom.
Using statistical tables for², t, F, and Z.
General concepts and notations concerning test of significant, Some significant tests based on:

Normal dist. (test for single mean, difference between two means).

t-dist. (test for single mean, difference between two means). ²– dist. (test for single variance, goodness of fit, the homogeneity of several variances).

F- dist. (test for the ration between two variances, one and two way analysis of variance). Test for regression coefficients.

ST401 : Mathematical Statistics I CREDITS 3

Introduction to distribution theory.( Cauchy, Laplace, Weibull, Logistic, Pareto and Gambel dist.)
Distributions of functions of random variables.
Expectations of functions of random variables( with referring to the mean and variance of such functions).
Concluding of distributions using.
1. Distribution function.
2. Moment generating
3. Transformation techniques.
Exact sampling distributions:

Derivation of chi-square, student-t and F-distributions.

Exact sampling distribution of the sample mean and variance from normal population.
Introduction to Order statistics, Weak law of large number, Central limit theorem.

ST402 : Sampling Techniques I CREDITS 3

Definitions
Purpose & advantages of sampling
Census versus sample surveys
Various stages of sample surveys
Random and non-random samples( with and without replacement )
Simple random sampling(properties of the estimates, tables of random numbers, sampling of proportions and percentages, confidence limits for the populations estimates, determination of sample size).
Stratified random sampling (notations, properties of the estimate, determination of sample size using proportional allocations, optimum allocation, Neyman allocation, confidence limits for the estimates, sampling of proportions and percentages)
relative precision of stratified sampling versus simple random sampling
Estimation of means and standard errors
Estimation of proportions

Estimation of sample size for a given precision.

ST403 : Correlation & Regression Analysis CREDITS 3

Bivariate Dist., Correlation
Scatter Diagram
Karl Person coefficient of correlation

Limits for Correlation coefficient

Assumptions underlying Karl Person coefficient of correlation

Probable Error of Correlation coefficient
Rank Correlation Repeated Ranks

Limits for the Rank Correlation coefficient

Concept and Assumptions of regression analysis.
Least square estimates and their properties including Gauss-Markov theorem.
Linear regression analysis
Point estimate of the parameters and their confidence intervals
Test of linearity of regression
Correlation coefficient between observed and Estimated Value, Correlation Ratio
Multiple and Partial Correlation ( properties, multiple Correlation can be expressed in terms of total and partial Correlation)

ST404 : Time Series Analysis CREDITS 3

Concept of time series, Objective of time series analysis, Kinds and components of time series, Time series Models.
Analysis of time series
Smoothing, Linear trend (Curve fitting, Filtering, differencing),

Moving average, Seasonal fluctuations, Cyclical fluctuations, Autocorrelation, Autocorrelation function (ACF), Interpreting the ACF .

Tests for linearity of time series, prediction, calculation of seasonal index.
Non-linear trend (2nd and 3rd degree, logarithmic, exponential, and logistic models)
Index numbers:
Concept, methods of constructions of index numbers
Sources of errors in constructing index numbers.
Standard of living.
Different tests of index numbers.

ST501 : Sampling Techniques II CREDITS 3

Introduction
Ratio and regression methods of estimation with and without stratification, Combined Ratio estimate
Difference and product estimation
Unbiased Ratio type estimate
Census verses sample surveys
Unbiased ratio type estimate
Systematic sampling
Single stage and cluster sampling
Estimation of means, totals & variance for simple random and stratified sampling
Ideas of unequal Probability sampling

ST502 : Theory Of Estimation CREDITS 3

Introduction
definitions of sample, population, parameter, statistic and estimator. Types of estimators
Point estimation :
Properties of estimator: unbiased, consistency, efficiency and sufficiency, minimum variance unbiased estimation
Methods of estimation: Method of Moments, Method of Maximum likelihood, Minimum variance, Least squares and Minimum chi-square, Mention of Bayesian method
Rao-Cramer Inequality Cauchy – Schwart’s Inequality
Interval estimation
Some fundamental notions of interval estimation, applications for obtaining confidence limits for parameters (means , variances and proportions, equal & Unequal, known & unknown population Variances) of some standard distributions (Normal).
Linear function of means of independent random sample,
Bayesian estimator and their uses

ST503 : Statistical Method II CREDITS 3

Scientific method of social survey
Natural and purpose of social survey
Important of research, formulation of research problem & hypothesis Field experiments and surveys, Types of survey, Designing survey.
Natural of Designing of laboratory experimentation, Collection of data.
Kind of questionnaires and canvass.

The problem of non-response, Field organization.

Training and supervision of field investigation.
Presentation of report, Familiarity with large sample surveys.

ST504 : Analysis Of Variance CREDITS 4

Concept and assumptions underlying ANOVA
One-way Analysis of Variance
Mathematical model
Fixed, mixed and random models.
Equal & unequal sample size, ANOVA tables, Expected of mean square
Test for homogeneity, Bartlette and Cochran transformations, Comparisons and contrasts, Least significant difference(LSD), Tukey method, Sheffe’ method, Duncan multiple range test.
Two-way Analysis of Variance
Mathematical model (without interaction & with interaction)
Fixed, random and mixed models.
ANOVA tables, Expected of mean square
Three way ANOVA
Mathematical model(without interaction & with interaction)
Fixed, random and mixed models.
ANOVA tables, Expected of mean square One-way-two factor ANOVA with and without replications.
Analysis of covariance one-way-one factor ANOCOV, two-way-one factor ANOCOV.

ST506 : Quality Control & Reliability CREDITS 3

Meaning and objective of Statistical Quality Control
Different techniques of achieving Statistical Quality Control
Different types Quality measures
Rational subgroups and technique of Quality Control charts (3 limits and probability limits, control charts for mean, S.D. and range , control charts for number of defectives, fraction defective and percent defective
Control Charts for attributes (P-chart & C-chart)
Control Charts for variables (P-chart & C-chart)
Operating characteristic curve. Acceptance sampling plans (single, double plans).
Meaning of Reliability

ST601 : Test Hypotheses CREDITS 3

Introduction, definitions and notations. Concept of simple and composite hypothesis, test of statistical Hypothesis, types of errors, power of a least, power function, Critical region.
Most powerful test and Uniformly most powerful lest, Neyman-Pearson lemma. Likelihood ratio test,
Determination of sample size, BCR, MP.
Applications (Tests about means, variances, proportions, regression, correlation coefficients Chi-square test: goodness of fit &independence).
Idea about SPRT, approximation expected sample size of a SPRT.

ST602 : Experimental Design CREDITS 4

definitions
Model, treatments, experimental unit, block, replication and experimental error
The rule of statistics: interpretation and analysis, Replication, randomization, Control of measurement of efficiency.
Completely Randomized designs: model, partitioning of Total

SS, ANOVA, Estimation of parameters, Multiple contrasts

(LSD, Tukey, Duncan, Scheffe’), (Equal & unequal replication), Analysis of covariance.

Randomized Blocks designs: model, partitioning of Total SS, ANOVA, (Equal & unequal replication), Estimation of parameters, Missing observations. Relative efficiency. Multiple contrasts, Analysis of covariance.
Latin Squares: model, orthogonal Latin Squares, partitioning of TSS, ANOVA, Estimation of parameters, Missing observations, relative efficiency.
Factor Experiments analysis of 2^p factorial experiments
Split-plot designs, incomplete Latin squares designs, balanced incomplete block designs.

ST603 : Regression Analysis CREDITS 3 •

Introduction.

Simple Regression model E(Y/X) & assumptions, estimation of, and inference (estimation & test) about the parameters, Angle between two lines of regression, Test of linearity of regression.
Multiple Regression. Matrix treatment. Estimation and inference about the parameters (estimation & test). Coefficient of determination. Polynomial regression with one regressors (predictor). Estimation of the parameters.

Orthogonal polynomial, determination of degree using ANOVA.
Search for best set of regressors (predictor) using Step-wise Method (Forward, Backward & Best R² ).
Duality Method

ST604 : Numerical Analysis CREDITS 3 •

Introduction

Source of error
Round errors and instability
Estimation of errors
Solution of Equations in one Variable
The bisection Algorithm
Fixed-point Iteration
The Newton-Raphson method
Zero of real Polynomials
Interpolation and polynomial Approximation
The Taylor Polynomials
Interpolation and lagrange Polynomial
Divided differences
Finite differences
Curve Fitting
Discrete least squares method
Cubic-spline method
Solving Linear systems
Gaussian Elimination and pivoting
Linear Algebra and Matrix Inversion
Direct Factorization of Matrices
Gauss iterative method
Numerical Solution of Non-Linear Systems
Fixed-point for function of several Variables – Newton’s method
Numerical Differentiation and Integration
Numerical differential – Higher derivatives and extrapolation
Elements of numerical integration – Composite numerical integration
Adaptive Quadratic Methods – Romberg Integration

ST702 : Mathematical Statistics II CREDITS 3

Introduction: Distributions of order statistics, Complex Numbers
Characteristic function (properties and related theorems Inversion theorem), Multivariate characteristic function
Infinite divisible law.
Chebyshev’s Inequality.
Concept of absolutely continuous random variables, sequence of random variables.
Modes of convergence:
Convergence in distribution.
Convergence in probability.
Mean square Convergence.
Limiting distribution and Stochastic Convergence.
Limiting moment generating function.
Laws of large numbers (Weak Law of large numbers WLLN).
Bernoulli’s law of large numbers.
Applications of law of large numbers.
Central limit theorem and it’s various forms.:
De-Moivere’s Laplace theorem.
Lindeberg-Levy theorem.
Liapounoff’s central limit theory.
Applications of Central limit theorem.

ST703 : Demography CREDITS 3

Introduction to vital statistics,
Collection of vital Statistics, Census, Mortality and fertility rates.
Construction of life table.
Types of population : Stationary, Stable and Dynamic Populations. Reproduction rates, Growth of population
Population projections and estimations.
Migration and distribution of population.

ST708 : Stochastic Processes CREDITS 3 •

Stochastic processes (definition & examples)

Markov Chain: one –two & multiple stats Markov chains, Transition functions, and initial distribution.
Transition and reconnect Stats.
Absorption Probabilities.
Continuous time Markov chains.
Birth & death chain.
Random walk (simple and general)
Unrestricted random walk with one or two absorbing barriers
Branching processes

ST803 : Sampling Distribution CREDITS 3 •

Introduction:

Gamma & Beta Distribution:( pdf, moments, moment generating function, Characteristic function, mode, Inflection points, skew ness, Additive property for Gamma Dist.)
Chi-Square distribution:( pdf, moments, moment generating function, Characteristic function, mode, Inflection points, skew ness, Additive property, test for population variance, Chi-Square test of independence & homogeneity, Chi-Square for pooling the probabilities, Yate’s correction)
Non-Central Chi-Square distribution: :(with non-central parameter, moment generating function, Additive property, Cumulate of nonCentral Chi-Square distribution)
Student’s t- distribution: (Derivation of Student’s t- distribution, pdf, moments, moment generating function, Characteristic function, mode, Inflection points, Critical values of t, Application of t-Dist.)
Non-Central Student’s t- distribution (properties)
F- distribution (Derivation of F- distribution, pdf, moments, moment generating function, Characteristic function, mode, Inflection points, Critical values of t, Application of F-Dist.)
Non-Central F- distribution (properties)

ST804 : Multivariate Analysis CREDITS 3

Introduction : Data Matrix (Mean vector, Covariance Matrix, Centering Matrix, Sample correlation Matrix, Linear Combinations, Transformation)
Basic properties of random vectors (cumulative dist., Joint density function, conditional dist., Expectation, Conditional moments, Characteristic function,)
Multi-normal Distribution (Quadratic form ,properties
Estimation of Mean vector and Covariance Matrix (Maximum likelihood estimators )
The distribution of the sample Mean Vector
Test and Confidence regions for mean vector
Non central Chi-Square distribution (Multivariate)
The General (Hotelling’s) T²– Statistics (properties) Wishart Distribution (properties)
Canonical Analysis.

ST806 : Operation Research CREDITS 3 •

Introduction: meaning and importance of Operation research

Linear Programming: General linear programming Problem , graphic solution, simplex method, Computational Procedure, Problem of degeneracy, duality in linear programming, Transportation problem, Assignment Problem, inventory problems.
Games theory : Kind of games, Two person-zero sum game, Stable Vs Unstable Game, Dominate Strategy.
Network Analysis: the critical path method CPM, PERT,
Queuing System: characteristics, Poisson & Exponential queues, models with numerical Examples.

ST809 : Applied Linear Models CREDITS 3 •

Introduction in Econometrics.

Problems of liner regression( autocorrelation- multicolinerity- heterscedasticity- error in variable).
Simultaneous equations.
Regression on :((Estimation of parameters in each case)):
Dummy variables (Dummy independent variables, Dummy dependent variable).

ST812 : Project I CREDITS 4

In this course the student (more than one student) chooses a problem for purpose of research. The statistical methods that he developed during the stages of his specialized studies are used.