Statistics I
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Course Title: Statistics I
Course No: STA169
Nature of the Course: Theory + Lab
Semester: 2
Full Marks: 60 + 20 + 20
Pass Marks: 24 + 8 + 8
Credit Hours: 3
Course Description
Course Objectives
Course Contents
1. Introduction
4 hrs
1.1. Fundamentals of Statistics
- Basic concept of statistics
- Application of Statistics in the field of Computer Science & Information technology
- Scales of measurement
- Variables
- Types of Data
- Notion of a statistical population
2.1. Statistical Measures
- Measures of central tendency
- Measures of dispersion
- Measures of skewness
- Measures of kurtosis
- Moments
- Stem and leaf display
- Five number summary
- Box plot
- Problems and illustrative examples related to computer Science and IT
3.1. Probability Theory
- Concepts of probability
- Definitions of probability
- Laws of probability
- Bayes theorem
- Prior and posterior probabilities
- Problems and illustrative examples related to computer Science and IT
4. Sampling
3 hrs
4.1. Sampling Concepts and Methods
- Definitions of population
- Sample survey vs. census survey
- Sampling error and non sampling error
- Types of sampling
5.1. Random Variable Theory
- Concept of a random variable
- Types of random variables
- Probability distribution of a random variable
- Mathematical expectation of a random variable
- Addition and multiplicative theorems of expectation
- Problems and illustrative examples related to computer Science and IT
6.1. Distribution Functions
- Probability distribution function
- Joint probability distribution of two random variables
6.2. Discrete Distributions
- Bernoulli trial
- Binomial distribution
- Poisson distribution
6.3. Continuous Distributions
- Normal distributions
- Standardization of normal distribution
- Normal distribution as an approximation of Binomial and Poisson distribution
- Exponential distribution
- Gamma distribution
- Problems and illustrative examples related to computer Science and IT
7.1. Correlation Analysis
- Bivariate data
- Bivariate frequency distribution
- Correlation between two variables
- Karl Pearson's coefficient of correlation(r)
- Spearman's rank correlation
7.2. Regression Analysis
- Fitting of lines of regression by the least squares method
- Coefficient of determination
- Problems and illustrative examples related to computer Science and IT
Laboratory Works
- 1.Computation of measures of central tendency (ungrouped and grouped data)
- 2.Computation measures of dispersion (ungrouped and grouped data) and computation of coefficient of variation
- 3.Measures of skewness and kurtosis using method of moments, Measures of Skewness using Box and whisker plot.
- 4.Scatter diagram, correlation coefficient (ungrouped data) and interpretation
- 5.Fitting of lines of regression
- 6.Fitting of lines of regression and computation of correlation coefficient, Mean residual sum of squares, residual plot.
- 7.Conditional probability and Bayes theorem
- 8.Obtaining descriptive statistics of probability distributions
- 9.Fitting probability distributions in real data
Text Books
- 1.Michael Baron (2013). Probability and Statistics for Computer Scientists. 2nd Ed., CRC Press, Taylor & Francis Group, A Chapman & Hall Book
- 2.Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, & Keying Ye (2012). Probability & Statistics for Engineers & Scientists. 9th Ed., Prentice Hall
Reference Books
- 1.Douglas C. Montgomery & George C. Ranger (2003). Applied Statistics and Probability for Engineers. 3rd Ed., John Wiley and Sons, Inc.
- 2.Richard A. Johnson (2001). Probability and Statistics for Engineers. 6th Ed., Pearson Education, India