 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

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

 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

 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

 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

 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

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

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

Collection, Organization, Summarization and Presentation of Data

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

 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

 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

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.

 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.

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

 The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:  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.

 Twenty Five soldiers were given a blood test to determine their blood type. The data set is: ABBABO OOBABB BBOAA AOOOAB ABAOBA

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

 Find the Variance and Standard Deviation for the Data Set:   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)

 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

 Represent the data by a Stem-and-Leaf Plot, a Histogram and a Boxplot:  Reaction Time [sec] of an automatic switch:

 Find the Mean and Compare it with Median.  Find the Standard Deviation and Compare it with the Interquartile Range:

 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, , 290

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

 The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:  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)