Course

Unit 1

Estimation theory – Point Estimation – Introduction- criteria of point estimation, unbiasedness, consistency, sufficiency, and efficiency of various distributions, method of maximum likelihood estimation and method of moments minimum risk estimators.

Unit 2

Interval Estimation: Introduction – confidence Interval for mean of a Normal Distribution with Variance known and unknown – Confidence Interval for the two means of a Normal Distribution with Variance known and unknown, Confidence interval for one and two Population Proportions, Confidence interval for the variance and ratio of variances.

Unit 3

Inference theory – introduction to hypothesis testing – large sample tests for single mean and two means – large sample tests for single proportion and two proportions.

Unit 4

Small sample tests for single mean and two means paired t-test – test for single variance test for equality of two variances.

Unit 5

Chi-square goodness of fit for Binomial, Poisson and Normal distributions, Independence of attributes, test for homogeneity, Non-parametric tests – sign test, signed rank test and Mann Whitney U test.

Text Books / References

Text Books:

1. George Casella & Roger L. Berger, Statistical Inference, Chapman & Hall/CRC Texts (2024).
2. Pradip Kumar Sahu, Santi Ranjan Pal & Ajit Kumar Das, Estimation and Inferential Statistics, (2016).
3. Friedrich Liese and Klaus-J. Miescke, Statistical Decision Theory: Estimation, Testing, and Selection, Springer Series in Statistics, (2010)

References

1. Ross S.M., Introduction to Probability and Statistics for Engineers and Scientists, 6^thedition, Elsevier Academic Press, (2021)
2. Ravichandran, J. Probability and Statistics for engineers, New Edition, Wiley India, 2023.

This course focuses on statistical estimation and inference techniques used in data science and research applications. It covers point estimation methods including maximum likelihood and method of moments, along with properties of estimators. The course introduces interval estimation and hypothesis testing for means, proportions, and variances under both large and small sample conditions. It also includes chi-square tests and non-parametric methods for real-world data analysis. The course equips students with analytical skills for statistical decision-making under uncertainty.

Course Outcomes: After successful completion of the course, students will be able to

• CO1: Apply principles of point estimation to determine unbiased, consistent, sufficient, and efficient estimators using methods of moments and maximum likelihood.
• CO2: Construct and interpret confidence intervals for population parameters including means, proportions, and variances under different conditions.
• CO3: Perform large sample hypothesis tests for means and proportions to support statistical decision-making.
• CO4: Conduct small sample tests including t-tests, paired t-tests, and F-tests for variances to analyze limited data samples.
• CO5: Apply chi-square tests and some non-parametric tests to assess goodness of fit, independence, and homogeneity in real-world data

CO-PO Mapping: