1- Probability set functions.
2- Random variables.
3- Special distributions.
4- Joint distributions.
5- Properties of random variables.
6- Distributions of functions of random variables.
7- Limiting distributions.
1. Point Estimation
2. Con¯dence Intervals
3. Testing of Statistical Hypotheses and Chi-Square Test.
4. Properties of Estimators.
5. Su±cient Statistic.
6. Completeness and uniqueness
7. Exponential Class of distributions
8. Multi-parameter Case Minimal Su±cient Statistic.
9. Bayesian Estimators
10. Roa-Cramer Bound
11. Asymptotic Distribution of Maximum Likelihood Estimators and Robust Estimation
12. Theory of Statistical Tests, UMP Tests, Likelihood Ratio Tests, The sequential Probability Ratio Tests,
Introduction to time series. Autocorrelated data. Stationary and trends. Time series components. Stochastic time series .Linear time series. Backshift operator. White noise process.
Autoregressive, moving average, and autoregressive moving average models. Random walk model. The Box -Jenkins notation. Integrated models. Differencing. General solution of linear difference equations. Unit roots.
Model identification. Autocorrelation and partial autocorrelation function. Model parameter estimation.
(1) Understand the concepts
(2) Analyze a certain data set using a specified procedure.
(3) Given a data set, select the proper statistical procedure to analyze it.
(4) Case study and report writing
(5) Suggest the proper design for a practical problem including data layout, analysis procedure, and recommendations.
(6) Communicate with statistical users and advice them with selecting the proper statistical procedure and reporting the results.
This course reviews the basic ideas from Algebra and Coordinate Geometry, and presents many opportunities for students to discover practical power of Mathematics. In particular, the course aims to:
1- Review basic concepts in Mathematics.
2- Prepare the students for calculus I, II, and III
3- Help students to become active learners.
4- Introduce students to applications of Mathematics.
Chapter 2 : Descriptive Statistics:
Measures of data centers and data variability
Some Vital Statistics Correlation Coefficient
Chapter 3 : Basic Probability and Conditional Probability Concepts
Chapter 4 : Probability Distributions
Binomial, Poisson ,Multinomial and Normal
Chapter 5 : Sampling Distributions
Chapter 6 : Estimation of Population Means,
Proportions and Differences
Chapter 7 : Hypothesis Testing
Chapter 8 : Analysis of Variance: One-way and two-way
Chapter 9 : Simple Linear Regression and Correlation
Chapter 12 : Chi-square and frequency Analysis
Independence and Homogeneity, probit analysis
Chapter 13 : Nonparametrics: Sign and Rank Tests
This course is a continuation for Calculus I. The course begins with Techniques of integration and it is given as: integration by parts, trigonometric integrals, trigonometric substitutions, partial fractions, rationalizations, half-angle substitution , and improper integrals. Then some applications of definite integrals are given such as: areas between two curves, volumes by washers and cylindrical shells, arc length, and area of a surface. The concept of infinite series is introduced, then tests of convergence are given. Power series, Maclaurin and Taylor expansions are given. Then differentiation and integration of power series are given. Finally, polar coordinates, graphs in polar coordinates, and areas in polar coordinates are given.