Course Code: MATH 2217-0542
Course Title: Probability & Statistics
Course Type: Theory
Prerequisite: MATH 1213-0541
Contact Hours: 42
Total Marks: 100
Statistics and probability deal with the study of collecting, analyzing, and presenting data which is essential in taking decisions and making predictions. This course is designed to provide theoretical knowledge regarding data collection and presentation in different techniques, measures of central tendency, dispersion, correlation and regression, sampling, probability, and its distributions.
1. Fundamentals of statistics:
Definitions of statistics - past and present, Its nature and characteristics, Meaning, Scope, and classification of statistics, Its relation with other disciplines, Limitations, Uses, Misuse, and abuse of statistics; Sources and types of statistical data, etc.
2. Data Collection:
Sampling and Related Issues: Sampling, probability and non-probability sampling, simple random sampling, stratified sampling, cluster sampling, systematic sampling, sampling error, non-sampling error, questionnaire, etc.
3. Organization and Presentation of Data:
Construction of frequency distribution, graphical methods on presentation of data using bar plot, pie chart, histogram, frequency polygon, ogive, stem and leaf plot, box and whisker plot, five number summaries, detection of outliers.
4. Statistical measurements:
Measures of Central Tendency, Measure of dispersion, and their applications.
5. Correlation and Regression:
Introduction, correlation, computation of simple coefficient of correlation, proof of variation of correlation, Scatter diagram, regression, regression lines, simple coefficient of regression, multiple and partial correlations.
6. Basic Concept of Probability:
Concepts of Probability, Sample space, Events, Laws of probability, Conditional probability; Baye’s theorem and its application, Random variables. Discrete and continuous random variables, Probability mass function, Probability density function.
7. Probability distribution:
Distribution function. Joint distribution, Marginal and Conditional distributions, Independence of random variables. Mathematical expectations Chebyshev’s inequality, Discrete and Uniform distribution, Binomial distribution, Poisson distribution, Negative Binomial distribution, Geometric distribution, Hypergeometric distribution, Continuous Uniform distribution, Exponential distribution, Normal distribution, Beta distribution, Gamma distribution, The Central Limit Theorem. Infinite Sequences of Random Variables The Gambler’s Ruin Problem.
Course Learning Outcomes (CLOs):
CLO1: Understand the background, scopes, and basic properties of statistics and probability.
CLO2: Analyze data, data collection, interpreting, and presenting and its probability how likely it will happen.
CLO3: Calculate and interpret statistical measurements, and the probability of any given event from given data.
CLO4: Use statistical knowledge and probability distribution in different practical situations frequently encountered in society, industry, commerce, trade, science, and technology, etc.,
CLO5: Develop statistical models and software for data analysis.
1. Mian M. A .and Mian M. A, Introduction to Statistics, 4th ed, Universal Press, Dhaka
2. Islam M. N. 2006. An Introduction to Statistics and Probability, Book World, Dhaka.
3. Mood, Graybill & Boes, Introduction to the theory of Statistics, 3rd ed. McGraw-Hill.
4. Hogg, R.V. & Craig, A.T. An Introduction to Mathematical Statistics, Mcm.-Colliern, N.Y
5. Sheldon M. Ross, 2007, Introduction to Probability Models, Elsevier, 9th Edition. N.Y.
6. M.K. Roy, 2019, Fundamentals of Probability & Probability Distribution, Romax Pub.s BD
Other Learning Materials: Journals, Web Materials, YouTube Videos, etc.