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Probability and Statistics BS-338. 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
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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
Course Objectives To teach students basics of Probability and Statistics with applications related to different disciplines of engineering.
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
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
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
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
Probability A probability provides a quantatative description of the likely occurrence of a particular event.
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
Descriptive Statistics Collection, Organization, Summarization and Presentation of Data
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
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
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
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.
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.
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
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.
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
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.
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)
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
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
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
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
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)
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)