1. Statistics and Probability Theory Lecture 01 Fasih ur Rehman

2. About Instructor MSc in Electronics and MSc in Systems Engineering in 1994 and 1996 respectively from Quaid-e-Azam University and currently pursuing PhD from CIIT Worked for Software Industry (developing engineering application) for 5+ years in Pakistan and abroad as well. Joined CIIT Wah Campus in 2003 as Assistant Professor and worked at various academic and administrative positions since then Research Interests Mathematical Modeling, Computational Electromagnetics

3. Course Contents Introduction to Statistics and Statistical Methods. Frequency distribution and representation of data. Measure of Central Tendency, Measure of Dispersion. Probability Theory: Counting Rules. Conditional Probability, Law of total probability and Bay’s Rule. Discrete and Continuous Random Variables. Cumulative Distributions, Joint Probability Distribution, Uniform, Binomial, Poisson Geometric, Normal, Gamma and Exponential Distributions. Simple Linear Regression and fitting curves. Correlation Study. Testing about Population Mean and Confidence Interval

4. Learning Outcome After successful completion of this course, a student should be able to –Define Statistics –Represent and Classify Data –Calculate and interpret means and other measures of central tendency –Define and calculate probabilities, work with random variables and various probability distributions –Apply various statistical techniques like regression analyses, correlation etc.

5. Why Statistics and Probability Analyses of Data in all fields –Sciences (Natural, Social and Management) –Engineering, Manufacturing and Industry –Governance (for surveys, planning and prediction)

6. Recommended Text Probability and Statistics for Engineers and Scientists 9 th Edition, by Walpole, Myers 2012 For Reference “Advanced Engineering Mathematics” by E Kreyszig (Chapters for Statistics and Probability)

7. Statistics According to Wikipedia “Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments”. Uncertainty in present in Data Variation in data Data collected is used for “Inferences” This information is used to improve the quality.

8. Statistical Methods Data: Data are values of qualitative or quantitative variable belonging to a set of items (Wikipedia). Data Collection –Simple Random Sampling Data collected in this process is called Raw Data –Experimental Design Problem Definition and issues to be addressed Demarcation of population of interest Sampling Definition of Experimental Design –Data Analyses –Statistical Inference

9. Data Representation Data can be represented –Numerically Numbers Grouped Data Tables –Graphically Curves Pie Chart Stem and Leaf plot Bar Chart / Histogram

10. Data Representation (Example) 89 84 87 81 89 86 91 90 78 89 87 99 83 89 Sort this data 78 81 83 84 86 87 87 89 89 89 89 90 91 99 Group this data –Make 5 groups GroupNo of Elements 75 - 791 80 - 843 85 - 897 90 - 942 94 - 991

11. Stem and Leaf Plot 89 84 87 81 89 86 91 90 78 89 87 99 83 89 The integer in 10s position is taken as stem –7, 8 and 9 will be used as stems The integers in unit positions will be regarded as leaf Leaf unit = 1.0 so

12. Summary Introduction to the course What is statistics and statistical methods Data and its representation