ST202 : Mathematical statistics

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

ST101ST102

Overview

This course introduces students to the basic concepts of random experiment, sample space, random variables and their types, the probability distribution function of a single random variable (discrete and continuous), and the cumulative probability distribution function. It also deals with mathematical expectation and variance, quantile, moment generating function, the most important discrete and continuous probability distributions. This course also aims at developing the student's ability to determine the probability distribution function of the binary random variable (discrete and connected), the marginal (marginal) probability distribution function, the joint cumulative probability distribution function, and the conditional probability distribution function, as well as knowledge of independent random variables, mathematical expectation, covariance, Correlation, functions of probability distributions of multiple random variables (discrete and continuous) and their properties.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Presentation of a discrete and continuous univariate (one-dimensional) random variable and their probability distributions

2. Explanation of the discrete and continuous binary random variable (with two dimensions) and their probability distributions

3.Identify some important probability distributions such as binomial, Poisson, normal distribution, and chi-square

4. Determine how to represent discrete and continuous probability distribution functions and the cumulative distribution function

5. Comparison of methods for calculating probabilities using the cumulative distribution function. Interpret and analyze statistical results and graphs of statistical data.

6. The link between the discrete and continuous random variable and their probability distributions

7. Proving some theories of probability, expectation, variance, and moment generation functions

8. Find out ways to calculate probabilities using the cumulative distribution function

9. Derive the expectation function, variance and cumulative distribution for the most important special distributions

10. Explanation and analysis of probability calculation methods using the cumulative distribution function

11. Solve a number of exercises and problems with more than one idea for a sample space and the events associated with it and the probabilities specified in each space

12.Give solutions to new, different, and multiple problems to find out the cumulative, expectation, variance, and moment's distributions functions

13. It can enable the student to extract the cumulative distribution function from the probability distribution function and vice versa

14. Calculate the expectation, variance and cumulative distribution function for the most significant special distributions

15. Use the basic rules of single and double integrals to solve some problems related to probability functions. The student should be able to present information and explain phenomena both orally and in writing.

Teaching and learning methods

1. Practical and theoretical lectures

2. Discussion and dialogue

3. Brainstorm

4. Working papers, case study

5. Presentations

6. Videos and e-learning

7. Using software and computer applications such as (MATLAB, Geogebra, Geometer)

Methods of assessments

Methods of evaluating students in this course are:

1. A written exam (essay + objective) = 30 marks, or its assessment is left to the course instructor.

2. Short exams (written or oral), demonstration assignments and presentation applications = 10 marks or the assessment is left to the course instructor.

3. Written final exam (essay + objective) = 60 marks

Main content of the Course

Week	Scientific subject	Number of hours	Lecture	Exercises
1	Sample space, random variable and its types	2	Ö	Ö
1	Discrete probability distributions and the probability mass function	2	Ö	Ö
2	Continuous probability distributions and the probability density function	2	Ö	Ö
2	Cumulative distribution, cumulative function and their properties	2	Ö	Ö
3	Mathematical expectation, variance and Chebyshev's inequality	4	Ö	Ö
4	Central an non-central moments and the moment generating function	4	Ö	Ö
5	First midterm exam (2 hours)
6	Joint probability distributions of two random variables	4	Ö	Ö
7	Joint probability mass function	2	Ö	Ö
7	joint probability density function	2	Ö	Ö
8	Joint mathematical expectation, covariance and correlation	4	Ö	Ö
9	Marginal distributions and joint distribution function	4	Ö	Ö
10	Second midterm exam (2 hours)
10-11	Conditional and independent distributions	4	Ö	Ö
11-12	Conditional expectation and conditional variance	4	Ö	Ö
12-13	Special discrete distributions	4	Ö	Ö
13-14	Special continuous distributions	4	Ö	Ö
15-16	Final exam
	Total	56

References:

Title of references	Publisher	Version	Author	Located
Applied Statistics	University of Tripoli	First	Dr. Ali Abd al Salam al Ammari Dr. Ali Hussein Al-Ajili	Public Libraries
Internet Sites	Basics of Mathematical Statistics			Google

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