probability and statistics notes

Pokhara University Semester 4 Probability & Statistics Handwritten Notes PDF Download

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**PROBABILITY AND STATISTICS**

ENSH 253
Lecture: 3 | Year: II
Tutorial: 1 | Part: II
Practical: 0

Course Objectives:
The objective of this course is to equip students with foundational knowledge in probability and statistics, focusing on core concepts essential for engineering applications. Students will develop essential skills in statistical data analysis, enabling them to apply various statistical techniques to address real-world engineering challenges. Additionally, the course emphasizes the interpretation and effective communication of statistical results, preparing students to make informed, data-driven decisions in their professional practice.

Descriptive Statistics and Basic Probability (6 hours)

Introduction to statistics and its importance in engineering
Measures of central tendency and measures of variation
Graphical representation of data: histograms, box plots, and scatter plots
Basic probability concepts, additive law, and multiplicative law
Conditional probability and Bayes’ theorem

Probability Distributions and Sampling Distribution (14 hours)

Random variables: discrete and continuous
Expectation and variance of discrete and continuous random variables
Discrete probability distributions: binomial, Poisson, and negative binomial
Continuous probability distributions: normal, gamma, and chi-square
Population and sample
Sampling distribution of mean and proportion
Central limit theorem

Statistical Inference (14 hours)

Point estimation and properties of estimators
Confidence intervals for means and proportions
Hypothesis testing, parametric and non-parametric tests, and procedures of hypothesis testing
Hypothesis testing of means: single mean, two means, paired t-test, and one-way analysis of variance (ANOVA)
Goodness-of-fit tests and independence of attributes: chi-square and Kolmogorov–Smirnov tests

Correlation and Regression (6 hours)

Correlation analysis and tests of linear correlation
Simple regression analysis and the concepts of explained, unexplained, and total variation
Multiple regression analysis

Statistical Quality Control (5 hours)

Quality control and its importance in engineering
Control charts for variables and attributes: X-bar chart, R-chart, and P-chart
Six Sigma concepts

Tutorial (15 hours)

Visualize data and compute measures of central tendency and variance in engineering problems using computer software.
Solve engineering problems involving probability.
Solve engineering problems involving discrete probability distributions and interpret the results.
Solve engineering problems involving continuous probability distributions and interpret the results.
Analyze numerical engineering datasets, perform normality tests, calculate confidence intervals, conduct significance tests of means, and perform ANOVA.
Analyze categorical engineering datasets, perform crosstabulation, conduct proportion and chi-square tests, and draw conclusions using computer software.
Calculate correlation coefficients and perform correlation tests on engineering data.
Fit and interpret simple and multiple regression models using engineering data and computer software.
Use control charts for process monitoring with sample engineering data.
Create control charts using computer software.

Final Exam
The questions will cover all chapters in the syllabus. The evaluation scheme will be as indicated below.

References

Ronald, E. W., Raymond, H. M., and Sharon, L. M. (2012). Probability & Statistics for Engineers & Scientists (9th edition). Boston, USA: Prentice Hall.
Richard, A. J. (2018). Probability and Statistics for Engineers (9th edition). Edinburgh Gate: Pearson Education Limited.
Sheldon, M. R. (2009). Introduction to Probability and Statistics for Engineers and Scientists (4th edition). London: Elsevier Inc.
Jay, L. D. (2012). Probability and Statistics for Engineering and Sciences. Boston: Thomson Brooks/Cole.
Brian, S. E., and Ibrsten, H. (2010). A Handbook of Statistical Analyses Using R (2nd edition). London: CRC Press, Taylor & Francis Group.
Andy, F. (2018). Discovering Statistics Using IBM SPSS Statistics (5th edition). London: SAGE Publications.

Probability and Statistics (ENSH 253) is an essential engineering course that develops the mathematical and analytical skills required to interpret data, evaluate uncertainty, and make informed engineering decisions. These IOE Notes cover the fundamental statistical methods and probability concepts needed by engineering students, with an emphasis on practical applications, numerical problem-solving, and data analysis.

The course begins with descriptive statistics, measures of central tendency and variation, graphical data representation, basic probability, conditional probability, and Bayes’ theorem. It then explores discrete and continuous random variables, probability distributions such as Binomial, Poisson, Normal, Gamma, and Chi-Square, sampling distributions, and the Central Limit Theorem. Statistical inference covers estimation, confidence intervals, hypothesis testing, t-tests, ANOVA, goodness-of-fit tests, and tests of independence. Students also study correlation, simple and multiple regression, and statistical quality control, including X-bar, R, and P control charts and Six Sigma concepts.

These Engineering Notes can help students understand statistical formulas, practise numerical problems, interpret engineering datasets, and strengthen their knowledge of data analysis using computer software. The tutorial topics also support practical learning in probability distributions, significance testing, regression modelling, and process monitoring.

For students seeking Pulchowk campus notes, Aerospace notes, and other engineering study materials, these subject-focused resources provide a structured approach to learning Probability and Statistics. Use these subject and semester notes to revise key concepts, practise important problem types, and prepare systematically for semester examinations.