2.  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. To teach students basics of Probability and Statistics with applications related to different disciplines of engineering.

4.  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.  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.  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.  Confidence Interva ls  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. A probability provides a quantatative description of the likely occurrence of a particular event.

9. 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. Collection, Organization, Summarization and Presentation of Data

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

13.  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 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. 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.  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. 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.  The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.42.54.82.93.6 2.83.35.63.72.8 4.44.85.25.04.8  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.  Twenty Five soldiers were given a blood test to determine their blood type. The data set is: ABBABO OOBABB BBOAA AOOOAB ABAOBA

20.  Carbon Content [%] of coal 8990898480 8890898890 8587868285 7689878686  Find the Range of above Data Set.  Formulate Frequency Distribution Table.  Represent the Data by a Histogram.

21.  Find the Variance and Standard Deviation for the Data Set:  106050304020  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.  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.  Represent the data by a Stem-and-Leaf Plot, a Histogram and a Boxplot:  Reaction Time [sec] of an automatic switch: 2.32.22.42.52.32.32.42.1 2.52.42.62.32.52.12.42.2 2.32.52.42.4

24.  Find the Mean and Compare it with Median.  Find the Standard Deviation and Compare it with the Interquartile Range: 2.32.22.42.52.32.32.42.1 2.52.42.62.32.52.12.42.2 2.32.52.42.4

25.  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.  The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.42.54.82.93.6 2.83.35.63.72.8 4.44.85.25.04.8  Represent the data by a Stem-and-Leaf Plot, and a Boxplot. (Marks: 2 +3)

27.  The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.42.54.82.93.6 2.83.35.63.72.8 4.44.85.25.04.8  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 Interquartile Range. Also graph its Stem-and- Leaf plot. (Rows 2, 4, 6)  (Marks: 2 +3)