Probability and Statistics
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Course Title: Probability and Statistics
Course No: BIT124
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
1.6. Organizing Numerical Data
- Ordered array
- Stem-and-Leaf display
- Frequency Distribution
1.7. Visualizing Categorical Data
- Bar Diagrams
- Pareto Charts
- Pie Chart
1.8. Visualizing Numerical Data
- Histogram
- Frequency polygon
- Cumulative Frequency Curve or Ogive
2.1. Measures of Central Tendency
- Mean
- Median
- Mode
2.2. Measures of Dispersion
- Range
- Semi-inter Quartile Range
- Standard Deviation and Coefficient of Variation
2.3. Measures of Shape
- Skewness (Using Karl Pearson's Method)
- Kurtosis (Using Percentile Method)
2.4. Exploratory Data Analysis
- Five Number Summary
- Box and Whisker Plot
3. Basic Probability
6 hrs
3.2. Basic Terminology Used in Probability
- Random Experiment or Trial
- Outcomes or Events
- Sample Space
- Mutually Exclusive Events
- Equally Likely Events
- Favorable Events
- Exhaustive Events
- Independent and Dependent Events
3.3. Definition of Probability
- Classical, Statistical, Subjective and Axiomatic Definitions
- Basic Principles of Counting, Permutation and Combinations
3.4. Laws of Probability
- Additive
- Multiplicative
3.5. Conditional Probability
- Marginal and Joint probability
- Statistical independence
4.1. Random Variables
- Concept of a Random Variable
- Types of Random Variables
- Probability Distribution of a Random Variable
- Mathematical Expectation of a Random Variable
4.2. Discrete Probability Distribution
- Binomial
- Poisson
- Geometric Distribution their Characteristic Features, Mean, and Variance
4.3. Continuous Probability Distribution
- Normal
- Standard Normal
- Exponential, and Pareto Distribution their Characteristic Features, Mean, and Variance
5. Estimation
6 hrs
5.5. Concept of Method of Maximum Likelihood Estimation (MLE)
- MLE for Parameters of Binomial, Poisson, Geometric Normal, Exponential, and Pareto Distribution
6.1. Hypothesis Testing Methodology
- The Null and Alternative Hypothesis
- Risks of Decision-Making using Hypothesis Testing
- Level of Significance
- Tails of a Test
- Regions of Rejection and Non-rejection
- Steps for Testing of Hypothesis
6.2. Test of Significance for Large Samples
- Z test of Hypothesis for One Mean (σ known or unknown)
- Z test for the Difference between Two Means
6.3. Test of Significance for Small Samples
- Assumptions and Application of t-distribution
- Degree of Freedom
- t-test of Hypothesis for One Mean
- t-test for the Difference between Two Means and Paired t-test
7.2. Methods of Studying Simple Correlation
- Scatter Diagram
- Karl Pearson's Coefficient of Correlation
7.4. Simple Linear Regression
- Determining the Simple Linear Regression Equation using Least Squares Method
Laboratory Works
- 1.Laboratory Works
Text Books
- 1.Levine, Stephan, Krehbiel and Berenson (2008), Statistics for Managers using Microsoft excel, 5th Edition, New Delhi: Prentice Hall of India.
- 2.Douglas A Lind, William G Marchal, Samuel A Wathen (2008), Statistical Techniques in Business and Economics, 13th edition, Tata McGraw-Hill India.
- 3.Douglas C. Montgomery & George C. Ranger (2003). Applied Statistics and Probability for Engineers. 3rd Ed., John Willey and Sons, Inc.
- 4.Richard A. Johnson (2001). Probability and Statistics for Engineers. 6th Ed., Pearson Education, India