كلية العلوم – جامعة سبها

Course Description

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 2p 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.

 

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