# Engineering Statistics

By Prof. Manjesh hanawal   |   IIT Bombay
Learners enrolled: 155
We have to deal with data all the time and it has to be analyzed in a systematic way to extract information. This course introduces all basic concepts in statistics and prepares one to use statistics in many engineering applications. Sound knowledge of statistics is important to develop good machine learning and artificial algorithms. This course will also focus giving exposure various statistical tools available in Python.

PREREQUISITES: Basic Probability

INDUSTRY SUPPORT: This is a basic course and will be recognized by all
Summary
 Course Status : Upcoming Course Type : Core Duration : 12 weeks Start Date : 23 Jan 2023 End Date : 14 Apr 2023 Exam Date : 29 Apr 2023 IST Enrollment Ends : 30 Jan 2023 Category : Multidisciplinary Credit Points : 3 Level : Undergraduate/Postgraduate

### Course layout

Week 1: Revising probability: Axioms of probability, Conditional probability, Baye’s theorem, Random Variable, commonly used distributions (continuous and discrete), Cumulative Distribution Function (CDF) and Probability Density Function (PDF) their properties
Week 2: Revising probability: Joint distributions, Function of random variables. Independence of Random Variables, Correlation of Random Variables, Correlation coefficient, Markov and Chebyshev inequality, Convergence of RVs, Limit theorems.
Week 3: Introduction to python. Data visualization and fitting data to a given distribution.
Week 4: Exponential Family of Distributions, Population and Random Sampling, Sample mean, variance and standard deviation, Sampling from Normal distribution, Student’s t-distribution, F-distributions
Week 5: Order Statistics, Generating Random Samples: Direct and Indirect methods, Accept Reject method,
Week 6: Metropolis Hastings algorithm, Generation of random samples using Python
Week 7: Data reduction principles, Sufficiency principle, Sufficient statistics, factorization theorem
Week 8: Point estimators: Likelihood functions, maximum likelihood estimator, Method of moments, Bayes method, Expectation Maximization (EM) methods, Consistency of estimators
Week 9: Bias, Mean squared error, Evaluating Estimators, Cramer’s Rao inequality, Information inequality, Fischer Information
Week 10: Hypothesis testing, Likelihood Ratio Test (LRT), Type-I and Type-II errors, Method of Evaluating Tests
Week 11: Interval Estimators, Confidence intervals, Simple Linear regression, multivariate regression, logistic regression, Goodness of fit,
Week 12: p-test, Kolmogorov-Smirnoff test, f-score and other statistical tests. Application of tests on sample datasets using Python.

### Books and references

1. Douglas C. Montgomery, Larry Faris Thomas and George C. Runger (2003) ``Engineering Statistics, 3rd edition, John Wiley & Sons.
2. Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer (2007) Mathematical Statistics with Applications, 7th edition, Duxbury Resource Center.
3. John A. Rice (1994) Mathematical Statistics and Data Analysis, 3rd edition, Thomson Learning
4. George Casella and Roger Berger (2004) Statistical Inference, 2nd edition, Thomson Learning

### Prof. Manjesh hanawal

IIT Bombay
Manjesh K. Hanawal received the M.S. degree in ECE from the Indian Institute of Science, Bangalore, India, in 2009, and the Ph.D. degree from INRIA, Sophia Antipolis, France, and the University of Avignon, Avignon, France, in 2013. After two years of postdoc at Boston University, he is now an Assistant Professor in Industrial Engineering and Operations Research at the Indian Institute of Technology Bombay, Mumbai, India. His research interests include performance evaluation, machine learning and network economics. He is a recipient of Inspire Faculty Award from DST and Early Career Research Award from SERB

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 29 April 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team