Probability and Statistics BS-338

1. Probability and StatisticsBS-338

2. Probability and Statistics • Catalogue No: BS-338 • Credit Hours: 3 • Text Book: Advanced Engineering Mathematics by E.Kreyszig • Reference Books • Probability and Statistics by Murray R. Speigel • Probability and Statistics for Engineers and Scientists by Walpole

3. Course Objectives To teach students basics of Probability and Statistics with applications related to different disciplines of engineering.

4. Course Outcomes • Present sample data and extract its important features • Understand different discrete and continuous probability distributions • Estimate different population parameters on the basis of samples • Implement quality control measures

5. Course Outline • Graphical Representation of Data: Stem-and-Leaf Plot, Histogram, and Boxplot • Mean, Standard Deviation, Variance • Sample Space, Experiment Outcomes, Sampling, and Set theory • Introduction to theory of Probability, and Conditional Probability • Permutations and Combinations

6. Course Outline • Random Variables and Probability Distributions • Mean and Variance of a Distribution, Expectation, Moments • Binomial, Poisson, Hypergeometric and Normal distributions • Distributions of several Random Variables • Random Sampling • Point Estimation of Parameters

7. Course Outline • Confidence Intervals • Testing of Hypothesis and Decisions • Quality Control and Control Charts • Acceptance Sampling, Errors and Rectification • Goodness of Fit and Chi-square Test • Regression Analysis

8. Probability A probability provides a quantatative description of the likely occurrence of a particular event.

9. Statistics Statistics is a discipline that allows researchers to evaluate conclusions derived from sample data. In practice, statistics refers to a scientific approach used to: • Collect Data • Interpret and Analyze Data • Assess the Reliability of Conclusions based on Sample Data

10. Descriptive Statistics Collection, Organization, Summarization and Presentation of Data

11. Inferential Statistics • Makes inferences from Samples to Population • Generalization from Samples to Population, Performing Estimates and Hypothesis Tests, Determining relationship among Variables, and making Predictions

13. Variable • A variable is an attribute that describes a person, place, thing, or idea • The value of the variable can "vary" from one entity to another

14. Qualitative vs Quantitative Variables • Qualitative variables take on values that are names or labels. The colour of a ball (e.g., red, green, blue) • Quantitative variables are numeric. They represent a measurable quantity. For example, population of a city

15. Discrete vs Continuous Variables Quantitative variables can be further classified as discrete or continuous. If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.

16. UnivariatevsBivariate Data • Univariate Data. A study that looks at only one variable, is said that we are working with univariate data. • Bivariate Data. A study that examines the relationship between two variables, is said working with bivariate data.

17. Problem Which of the following statements are true? • I. All variables can be classified as quantitative or categorical variables. II. Categorical variables can be continuous variables. III. Quantitative variables can be discrete variables. • (A) I only (B) II only (C) III only (D) I and II (E) I and III

18. Problem • The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.8 5.2 5.0 4.8 • What is the sample size for the above sample? • Calculate the Sample Mean for this data. • Calculate the Sample Median • Compute the 20% trimmed mean for the above Data Set.

19. Categorical Frequency Distribution • Twenty Five soldiers were given a blood test to determine their blood type. The data set is: A B B AB O O O B AB B B B O A A A O OO AB AB A O B A

20. Grouped Frequency Distribution • Carbon Content [%] of coal 89 90 89 84 80 88 90 89 88 90 85 87 86 82 85 76 89 87 86 86 • Find the Range of above Data Set. • Formulate Frequency Distribution Table. • Represent the Data by a Histogram.

21. Problem • Find the Variance and Standard Deviation for the Data Set: • 10 60 50 30 40 20 • Steps to calculate Variance and Standard Deviation • Find the Mean • Subtract the Mean from each Data Value • Square each result • Find sum of squares • Divide sum by N to get the Variance (291.7) • Take Square Root, to find Standard Deviation (17.1)

22. Problem • Draw a Stem-and-Leaf Plot and Box-and-Whisker Plot for the following set of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41

23. Problem Set 24.1Question 7 • Represent the data by a Stem-and-Leaf Plot, a Histogram and a Boxplot: • Reaction Time [sec] of an automatic switch: 2.3 2.2 2.4 2.5 2.3 2.3 2.4 2.1 2.5 2.4 2.6 2.3 2.5 2.1 2.4 2.2 2.3 2.5 2.4 2.4

24. Problem • Find the Mean and Compare it with Median. • Find the Standard Deviation and Compare it with the Interquartile Range: 2.3 2.2 2.4 2.5 2.3 2.3 2.4 2.1 2.5 2.4 2.6 2.3 2.5 2.1 2.4 2.2 2.3 2.5 2.4 2.4

25. Problem • Complete a stem-and-leaf plot for the following list of values: 100,  110,  120,  130,  130,  150,  160,  170,  170, 190, 110,  230,  240,  260,  270,  270,  280.  290,  290

26. QUIZ # 1DE-32(B) – 17 SEP 2012 • The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.8 5.2 5.0 4.8 • Represent the data by a Stem-and-Leaf Plot, and a Boxplot. (Marks: 2 +3)

27. QUIZ # 1DE-32(A) – 18 SEP 2012 • The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.8 5.2 5.0 4.8 • Make a Frequency Distribution Table and represent the data by a Boxplot. (Rows 1, 3, 5) • Find the Standard Deviation and Compare it with the InterquartileRange. Also graph its Stem-and-Leaf plot. (Rows 2, 4, 6) • (Marks: 2 +3)